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![Online Geometry](../problem/h_geometry_problem_810.jpg)
Plane Geometry: Diameters and Chords, Theorems and Problems
Diameters, chords meet,
Geometry's harmony,
Theorems intertwine.
Problems unravel their depths,
Lines and arcs hold secrets vast.
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![Diameters and Chords on a Circle](diameters_chords_1.jpg) |
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![Geometry Problem 1569](../school-college/6/p1569-isosceles-triangle-square-relationship-diameter-incircle-tutoring-1.jpg) |
Geometry Problem 1569:
Prove a Relationship: EG Equals the Incircle Diameter in Triangle ABC with Square CDEF. |
![Geometry Problem 1567](../school-college/6/p1567-bases-isosceles-trapezoid-circumscribed-circle-chord-distance-measurement-tangent-tutoring-1.jpg) |
Geometry Problem 1567:
Finding Tangent Distances in a Circumscribed Isosceles Trapezoid. |
![Geometry Problem 1561](../school-college/6/p1561-highschool-college-geometry-triangle-ABC-circumcenter-orthocenter-angle-parallel-problem-1.jpg) |
Geometry Problem 1561:
Triangle ABC, Circumcenter O, Orthocenter H, Parallel Line, and Angle
Secrets. |
![Geometry Problem 1556](../school-college/6/p1556-right-triangle-inscribed-circle-properties-and-length-of-FG-problem-solving-1.jpg) |
Geometry Problem 1556: Right Triangle ABC and Inscribed Circle. The problem involves circle, chords, tangent, perpendicular lines, and congruence |
![Geometry Problem 1555](../school-college/6/p1555-circle-chord-intersect-geometry-problem-solving-1.jpg) |
Geometry Problem 1555: Find Length of DE. The problem involves chords, tangent, circles, and intersections of line |
![Geometry Problem 1544](../school-college/6/p1544-calculate-area-triangle-with-given-arc-semicircle-intersection-geometry-resource-1.jpg) |
Geometry Problem 1544: Challenge: Calculate the Area of a Triangle with Given Arc and Semicircle Intersections. |
![Geometry Problem 1541](../school-college/6/p1541-inscribed-cyclic-quadrilateral-diameter-circumcircle-harmonic-quaternary-menelaus-ceva-1.jpg) |
Geometry Problem 1541 Challenge: Unveiling BG Length in an Inscribed Quadrilateral with Harmonic Quaternary Insight for Academic Pursuit. |
![Geometry Problem 1540](../school-college/6/p1540-length-chord-circle-intersection-diameter-similarity-math-class-1.jpg) |
Geometry Problem 1540: Solving for the Length of Chord in a Circle: Analyzing Intersections and Given Values for Academic Pursuits. |
![Geometry Problem 1539](../school-college/6/p1539-isosceles-triangle-tangent-circle-altitude-right-angle-midpoint-measurement-math-class-1.jpg) |
Geometry Problem 1539 Demystified: Unraveling the Lengths in an Isosceles Triangle with Altitude and Tangent Secrets!. |
![Geometry Problem 1532](../school-college/6/p1532-square-inner-semicircle-tangent-find-angle-chord-1.jpg) |
Geometry
Problem 1532: Crack the Code of Geometry Problem 1532: How to Find the Angle in a Square with a Tangent Semicircle! - A High School Challenge.
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![Geometry Problem 1531](../school-college/6/p1531-circle-diameter-chord-angle-pythagorean-theorem-length-30-degree-1.jpg) |
Geometry
Problem 1531: Discover How to Calculate the Length of a Chord in a Circle with Diameter Intersection and an Angle between the Diameter and Chord - A High School Challenge.
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![Geometry Problem 1527](../school-college/6/p1527-two-intersecting-circles-angle-between-chords-1.jpg) |
Geometry
Problem 1527: Discovering the Hidden Angle: Solving the Puzzle of Two Intersecting Circles.
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![Geometry Problem 1521](../school-college/6/p1521-triangle-find-angle-side-two-diameter-circle-1.jpg) |
Geometry
Problem 1521 and a Thematic Poem.
Unlock the Secret to Finding the Measure of an Angle in a Triangle with Two Sides as Diameters of Circles. |
![Geometry Problem 1498](../school-college/5/p1498-intersecting-circles-diameter-common-chord-secant-cyclic-quadrilateral-concyclic-collinear-points-1.jpg) |
Geometry
Problem 1498.
Intersecting Circles, Diameter, Common Chord, Secant, Cyclic Quadrilateral, Concurrent Lines, Concyclic and Collinear Points. |
![Geometry Problem 1495](../school-college/5/p1495-circle-parallel-chords-30-degree-square-radius-1.jpg) |
Geometry
Problem 1495.
Circle, Parallel Chords, 30 Degree Angle, Radius Squared. |
![Geometry Problem 1485](../school-college/5/p1485-triangle-altitude-orthocenter-circle-tangent-measurement-1.jpg) |
Geometry
Problem 1485.
Triangle, Orthocenter, Altitude, Circle, Diameter, Tangent, Measurement. |
![Dynamic Geometry 1479](../school-college/5/p1479-triangle-circumcircle-angle-perpendicular-bisector-parallel-concyclic-geogebra-ipad-1.jpg) |
Dynamic Geometry 1479.
Triangle, Circumcircle, Angle Bisector,
Perpendicular Bisector, Chord, Concyclic Points, Parallel Lines,, Step-by-step Illustration. GeoGebra,
iPad. |
![Dynamic Geometry 1474](../school-college/5/p1474-butterfly-theorem-circle-chord-midpoint-geogebra-ipad-1.jpg) |
Dynamic Geometry 1474.
Butterfly Theorem, Circle, Chords, Midpoints, Step-by-step Illustration. |
![Geometry Problem 1453](../school-college/5/p1453-circle-diameter-cyclic-quadrilateral-concyclic-1.jpg) |
Geometry
Problem 1453.
Two Semicircles, Cyclic Quadrilateral, Concyclic Points,
iPad. |
![Dynamic Geometry 1449](../school-college/5/p1449-salmon-line-geogebra-dynamic-geometry-igs-1.jpg) |
Dynamic Geometry 1449.
Salmon Line. Step-by-step
illustration using GeoGebra. |
![Problem 1439](../school-college/5/p1439-rectangle-diagonal-perpendicular-circle-ipad-apps-1.jpg) |
Geometry Problem 1439.
Rectangle, Diagonal, Perpendicular, Circles, Areas, Art, Poster, Typography, iPad Apps. |
![Problem 1435](../school-college/5/p1435-circle-diameter-tangent-parallelogram-1.jpg) |
Geometry Problem 1435.
Circle, Diameter, Inscribed Circles, Circular Sector, Parallelogram, Parallel Lines, Tangency Points,
Poster, Typography, iPad Apps. |
![Problem 1431](../school-college/5/p1431-apollonius-llc-triangle-circumcircle-tangent-congruent-angle-1.jpg) |
Geometry Problem 1431.
Triangle, Circumcircle, Parallel Chord, Apollonius, LLC, Congruent Angles, Poster, Conformal Mapping. |
![Problem 1402](../school-college/5/p1402-triangle-three-tangent-circles-diameter-collinearity-tutor-1.jpg) |
Geometry Problem 1402. Triangle, Three Tangent Circles, Parallel Diameter, Collinear Points. |
![Problem 1401](../school-college/5/p1401-rigth-triangle-isosceles-tangent-congruence-tutor-1.jpg) |
Geometry Problem 1401. Right Triangle with three circles on the sides, Isosceles, Diameter, Center, Tangent, Congruence. |
![Problem 1397](../school-college/4/p1397-circle-tangent-90-degree-collinear-tutoring-1.jpg) |
Geometry Problem 1397. Circle, Diameter, Tangent, Secant, 90 Degrees Angle,
Perpendicular, Collinear Points. |
![Problem 1382 Circle, Diameter, Radius, Perpendicular, Congruence](../school-college/4/p1382-circle-diameter-perpendicular-congruence-tutoring-1.jpg) |
Geometry Problem 1382. Circle, Diameter, Radius, Perpendicular, Congruence. |
![Problem 1380 Circles, Tangents, Chords](../school-college/4/p1380-two-circle-common-internal-tangent-congruent-chord-1.jpg) |
Geometry Problem 1380. Common
Internal Tangents. Circles, Secant, Congruent Chords. |
![Problem 1379 Circles, Tangents, Chords](../school-college/4/p1379-two-circle-common-external-tangent-congruent-chord-1.jpg) |
Geometry Problem 1379. Common External Tangents. Circles, Secant, Congruent Chords. |
![Geometry problem 1365](../school-college/4/p1365-circle-chord-parallel-secant-tangent-midpoint-1.jpg) |
Geometry Problem 1365.
Circle, Tangent, Secant, Chord, Parallel, Midpoint, Sketch, iPad Apps. |
![Geometry problem 1355](../school-college/4/p1355-triangle-median-circle-measurement-tutoring-1.jpg) |
Geometry Problem 1355.
Triangle, Midpoint, Median, Circle, Chord, Equal Product of measure of segments. |
![Geometry problem 1354](../school-college/4/p1354-circle-tangent-secante-parallel-tutoring-1.jpg) |
Geometry Problem 1354. Circle, Tangent Lines, Secant, Chord, Center, Parallel Lines. |
![Geometry problem 1353](../school-college/4/p1353-tangent-circle-congruence-30-degrees-1.jpg) |
Geometry Problem 1353. Tangent Circles, Perpendicular Diameters, Congruence, 30 Degrees. |
![Geometry problem 1343](../school-college/4/p1343-triangle-excircle-tangent-90-degree-1.jpg) |
Problem 1343.
Triangle, Excircles, Circle, Tangent, Tangency Points, Chord, Perpendicular, 90 Degrees, Collinearity. Machu Picchu in the background.
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![Geometry problem 1342](../school-college/4/p1342-circle-chord-secant-parallel-midpoint-cyclic-1.jpg) |
Problem 1342.
Circle, Secant, Chord, Midpoint, Concyclic Points, Cyclic Quadrilateral.
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![Geometry problem 1321](../school-college/4/p1321-intersecting-circles-diameter-collinearity-1.jpg) |
Geometry Problem 1321.
Intersecting Circles, Diameter, Secant, Chord, Collinearity. |
![Geometry problem 1281](../school-college/3/p1281-triangle-circle-diameter-tangent-angle-bisector-tutoring-1.jpg) |
Geometry Problem 1281.
Triangle, Circle, Diameter, Tangent, Altitude, Congruent Angles. |
![Geometry problem 1261](../school-college/3/p1261-cyclic-quadrilateral-angles-3-4-5-1.jpg) |
Geometry Problem 1261.
Cyclic Quadrilateral, Circle, Diameter, Midpoint, Measurement. |
![Geometry problem 1259](../school-college/3/p1259-triangle-circle-diameter-parallel-1.jpg) |
Geometry Problem 1259.
Triangle, Circumcircle, Circle, Diameter, Parallel Lines. |
![Geometry problem 1251](../school-college/3/p1251-triangle-circle-diameter-90-degrees-1.jpg) |
Geometry Problem 1251.
Triangle, Circle, Diameter, Perpendicular, 90 Degrees. |
![Geometry problem 1250](../school-college/3/p1250-cyclic-quadrilateral-circle-diameter-congruence-1.jpg) |
Geometry Problem 1250.
Cyclic or Inscribed Quadrilateral, Circle, Diameter, Congruence. |
![Geometry problem 1191](../school-college/2/p1191-circle-chord-diameter-congruence-bisector-1.jpg) |
Geometry Problem 1191
Circle, Chords, Diameter, Congruence, Midpoint, Collinearity, Bisector. |
![Geometry problem 1190](../school-college/2/p1190-circle-chord-congruence-tutoring-1.jpg) |
Geometry Problem 1190
Circle, Chords. Congruence. |
![Geometry problem 1181](../school-college/2/p1181-quadrilateral-tangential-cyclic-diameter-problem-solving-1.jpg) |
Geometry Problem 1181
Cyclic Quadrilateral and Tangential Quadrilateral, Diameter as a Diagonal, Incenter, Circumcenter. |
![Geometry problem 1151](../school-college/2/p1151-circle-diameter-chord-perpendicular-90-degrees-1.jpg) |
Geometry Problem 1151.
Circle, Diameter, Chord, Perpendicular, 90 Degrees, Metric Relations. |
![Geometry Problem 1090](../school-college/1/p1090-circle-diameter-perpendicular-chord-metric-relations-tutoring-math-1.jpg) |
Geometry Problem
1090.
Circle, Diameters, Chord, Perpendicular, Metric Relations. |
![Geometry Problem 1084](../school-college/1/p1084-circle-chord-parallel-45-degrees-radius-metric-relations-triangle-class-math-1.jpg) |
Geometry Problem
1084.
Circle, Chord, Radius, Diameter, Parallel lines, 45 Degrees, Metric Relations. |
![Geometry Problem 1083](../school-college/1/p1083-circle-perpendicular-tangent-metric-relations-triangle-class-math-1.jpg) |
Geometry Problem
1083.
Semicircle, Diameter, Perpendicular, 90 Degrees, Tangent Line, Metric Relations. |
![Geometry Problem 1071](../school-college/1/p1071-arbelo-circle-semicircle-perpendicular-tangent-midpoint-problem-solving-tutor-1.jpg) |
Geometry Problem
1071.
Arbelos, Semicircles, Diameter, Circle, Perpendicular, Common Tangent, Parallel, Collinear Points, 90 Degrees,
Midpoint. |
![Geometry Problem 1070](../school-college/1/p1070-circle-square-rectangle-area-problem-solving-tutorial-1.jpg) |
Geometry Problem
1070.
Circle, Chord, Equilateral Triangle, Square, Rectangle, Area, Diameter, Perpendicular. |
![Geometry Problem 1058](../school-college/1/p1058-triangle-sum-area-altitude-circle-diameter-perpendicular-math-1.jpg) |
Geometry Problem
1058.
Triangle, Sum of the Areas, Altitude, Perpendicular, Circumcircle, Circle, Diameter. |
![Geometry Problem 1057](../school-college/1/p1057-circle-tangent-secant-diameter-perpendicular-area-math-1.jpg) |
Geometry Problem
1057.
Triangle, Area, Circle with Perpendicular Diameters, Tangent, Secant. |
![Geometry Problem 1048](../school-college/1/p1048-tangent-circles-common-tangent-chord-metric-relations-math-1.jpg) |
Geometry Problem
1048.
Circles, Tangent, Perpendicular, Diameter, Angle Bisector. |
![Geometry Problem 1033](../school-college/1/p1033-triangle-obtuse-circumcircle-diameter-area-math-1.jpg) |
Geometry Problem
1033.
Triangle, Angle Obtuse, Circumcircle, Diameter, Area. |
![Geometry Problem 1019](../school-college/1/p1019-circle-tangent-secant-diameter-chord-sum-math-1.jpg) |
Geometry Problem
1019.
Circle, Diameter, Perpendicular, Chord, Tangent, Sum. |
![Geometry Problem 951](../school-college/p951-intersecting-circles-tangent-diameter-parallel-cyclic-quadrilateral-1.jpg) |
Geometry Problem 951.
Intersecting Circles, Chord, Diameter, Parallel, Cyclic Quadrilateral, Concyclic Points. |
![Triangle, Orthocenter, Circumcircle, Diameter, Midpoint](../school-college/p783-triangle-orthocenter-circumcircle-diameter-midpoint-1.jpg) |
Geometry Problem 783
Triangle, Orthocenter, Circumcenter, Circumcircle, Diameter, Altitude, Midpoint. |
![Triangle, Orthocenter, Circumcircle, Diameter, Altitude, Parallelogram](../school-college/p782-triangle-orthocenter-circumcircle-diameter-parallelogram-1.jpg) |
Geometry Problem 782
Triangle, Orthocenter, Circumcenter, Circumcircle, Diameter, Altitude, Parallelogram. |
![Triangle, Distance from the Orthocenter to a Vertex, Circle, Circumradius, Side, Square.](../problem/p778-triangle-altitude-orthocenter-vertex-circumradius-side-1.jpg) |
Geometry Problem 778
Triangle, Distance from the Orthocenter to a Vertex, Circle, Circumradius, Side, Square. |
![Isosceles Triangle, Circle, Diameter, Altitude, Chord](../problem/p760-isosceles-triangle-circle-diameter-metric-relations-1.jpg) |
Geometry Problem 760
Isosceles Triangle, Circle, Diameter, Altitude, Chord, Metric relations. |
![Tangent Circles, Incenter, Chord](../problem/p713_tangent_circles_1.jpg) |
Geometry Problem
713.
Tangent Circles, Diameter, Chord, Tangent, Incenter, Incircle, Triangle. |
![Semicircles, Tangent, Perpendicular, Angle](../problem/p712_tangent_circles_1.jpg) |
Geometry Problem
712.
Semicircle, Diameter, Tangent, Perpendicular, Angle Measure. |
![Circle, Area, Tangent, Intersecting, Lune](../problem/p708_circle_area_lune_1.jpg) |
Geometry Problem
708.
Circle, Tangent, Intersecting, Lune, Area, Diameter. |
![Intersecting Circles, Diameter](../problem/p705_intersecting_circles_1.jpg) |
Geometry Problem
705.
Intersecting Circles, Diameter, Angles, Measurement. |
![Intersecting Circles, Diameter, Perpendicular](../problem/p701_circles_angles_1.jpg) |
Geometry Problem
701.
Intersecting Circles, Diameter, Perpendicular, Angles, Congruence. |
![Concentric Circles](../problem/p680-concentric-circles-1.jpg) |
Geometry Problem 680.
Concentric Circles, Radii, Chords, Perpendicular, Metric Relations. |
![Circles, Diameter, Tangent, Metric Relations](../problem/p676-circle-metric-relatio1.jpg) |
Geometry Problem 676.
Circles, Diameter, Tangent, Chord, Metric Relations. |
![Tangent Circles, Geometric Mean](../problem/p672_tangent_circles_1.jpg) |
Geometry Problem 672.
Internally tangent circles, Chord, Tangent, Geometric Mean. |
![Triangle, Altitudes, Circles, Angles](../problem/p658_triangle_circle_1.jpg) |
Geometry Problem 658.
Triangle, Altitudes, Diameter, Circle, Angles. |
![Online Math: Geometry Problem 571, Circle](../problem/p571_circle_diameter_1.jpg) |
Problem
571.
Circle, Diameter, Chord, Perpendicular, Measurement. |
![Cyclic quadrilateral, Diagonal, Diameter](../problem/p530_cyclic_quadrilateral_1.jpg) |
Problem 530.
Cyclic Quadrilateral, Diagonal, Diameter, Chord, Perpendicular, Congruence. |
![Right Trapezoid, Circle, Diameter](../problem/p529_trapezoid_circle_1.jpg) |
Problem 529.
Right Trapezoid, Circle, Diameter, Chord. |
![Circle, Tangent, Diameter, Radius, Congruence](../problem/p525_circle_tangent.jpg) |
Problem 525.
Circles, Diameter, Chord, Tangent, Radius, Congruence, Measurement. |
![Tangent Circles](../problem/p523_tangent_circle_1.jpg) |
Problem 523.
Tangent Circles, Diameter, Chord, Perpendicular, Collinearity. |
![Geometry Problem: Right triangle, Circle, Tangent](../problem/p522_triangle_circle_1.jpg) |
Problem 522.
Right Triangle, Circle, Diameter, Chord, Tangent. |
![Circle, Diameter, Chord, Perpendicular](../problem/p500_circle_diameter_1.jpg) |
Problem 500.
Circle, Diameter, Chord, Perpendicular, Measure. |
![Circle, Area, 90 Degrees](../problem/p487_circle_area_1.jpg) |
Problem 487.
Intersecting Circles, Area, Diameter and Chord, Parallel, 90 Degrees. |
![Triangle, circle, angle, altitude](../problem/p480_circle_angle_1.jpg) |
Problem 480.
Triangle, Circle, Center, Diameter, Chord, Altitude, Angle, Circumcenter. |
![Triangle, Sides, Circumradius](../problem/p478_triangle_circle_1.jpg) |
Problem 478.
Triangle, Sides, Circumradius, Circumcenter, Circumcircle, Diameter, Chord. |
![Three tangent circles](../education/p456_tangent_circles_1.jpg) |
Proposed Problem 456.
Three tangent circles, Center, Chord, Secant, Collinear, Diameters and Chords. |
![Tangent circles, diameter](../problem/p448_tangent_circle_1.jpg) |
Proposed Problem 448.
Tangent Circles, Diameter, Perpendicular, Chord. |
![Tangent Circles, Chords, Perpendiculars](../problem/p438_circle_chord_1.jpg) |
Proposed Problem 438.
Tangent Circles, Diameter, Chord, Perpendicular, Congruence,
Measurement, Parallel lines. |
![Tangent Circles, Chords, Perpendiculars](../problem/p437_circle_chord_1.jpg) |
Proposed Problem 437.
Tangent Circles, Diameter, Chord, Perpendicular, Congruence,
Measurement. |
![Tangent Circles, Chords, Perpendiculars](../problem/p436_circle_chord_1.jpg) |
Proposed Problem 436.
Tangent Circles, Diameter, Chord, Perpendicular, Congruence,
Measurement. |
![Problem about square and inscribed circle](../problem/p373_square_circle_angle_17.jpg) |
Proposed Problem 373.
Square, Inscribed Circle, Diagonal, Perpendicular, Angle, Diameters and Chords. |
![Triangle area, Circle, Curvilinear triangle](../problem/p364_triangle_area_17.jpg) |
Proposed
Problem 364.
Obtuse triangle, Congruence, Circles, Diameter, Chord, Curvilinear triangle,
Area. |
![Circle and Inscribed Semicircle](../problem/p333_circle_semicircle_17.jpg) |
Proposed Problem 333.
Circle inscribed in a semicircle, Perpendicular to the common tangent, Diameters and Chords. |
![Triangle, Altitudes, Concyclic Points](../problem/p329_triangle_altitude_17.jpg) |
Proposed Problem 329.
Triangle, Altitudes, Circle, Diameter, Concyclic points, Diameters and Chords. |
![Circle inscribed in a semicircle](../problem/p310_circle_semicircle_17.jpg) |
Proposed Problem 310.
Circle Inscribed in a Semicircle, 45 Degrees Angle, Diameters and Chords. |
![Right Triangle Circumcenter, Excenter](../problem/p294_triangle_excenter_17.jpg) |
Proposed Problem 294.
Right triangle, Circumcenter, Excenter, Hypotenuse, Perpendicular, Diameters and Chords. |
![Cube of the external common tangent](../problem/p272_tangent_circles_17.jpg) |
Proposed Problem
272.
Tangent Circles, the Cube of the Common external tangent, Diameters and Chords. |
![Cube of the external common tangent](../problem/p271_tangent_circles_17.jpg) |
Proposed Problem
271.
Tangent Circles, the Cube of the Common external tangent, Diameters and Chords. |
![Elearning 190 tangent circles, chord, perpendicular](../problem/p190_tangent_circles_17.jpg) |
Proposed Problem 190. Tangent
circles, Tangent chord, Perpendicular, Distance, Intersection of a Line
with a Circle, Diameter. |
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Email | by Antonio Gutierrez
Last updated:
Jul 24, 2024
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