Online Geometry

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.

Diameters and Chords on a Circle


Geometry Problem 1561

Geometry Problem 1561: Triangle ABC, Circumcenter O, Orthocenter H, Parallel Line, and Angle Secrets.

Geometry Problem 1556

Geometry Problem 1556: Right Triangle ABC and Inscribed Circle. The problem involves circle, chords, tangent, perpendicular lines, and congruence

Geometry Problem 1555

Geometry Problem 1555: Find Length of DE. The problem involves chords, tangent, circles, and intersections of line

Geometry Problem 1544

Geometry Problem 1544: Challenge: Calculate the Area of a Triangle with Given Arc and Semicircle Intersections.

Geometry Problem 1541

Geometry Problem 1541 Challenge: Unveiling BG Length in an Inscribed Quadrilateral with Harmonic Quaternary Insight for Academic Pursuit.

Geometry Problem 1540

Geometry Problem 1540: Solving for the Length of Chord in a Circle: Analyzing Intersections and Given Values for Academic Pursuits.

Geometry Problem 1539

Geometry Problem 1539 Demystified: Unraveling the Lengths in an Isosceles Triangle with Altitude and Tangent Secrets!.

Geometry Problem 1532

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.

Geometry Problem 1531

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.

Geometry Problem 1527

Geometry Problem 1527: Discovering the Hidden Angle: Solving the Puzzle of Two Intersecting Circles.

Geometry Problem 1521

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

Geometry Problem 1498.
Intersecting Circles, Diameter, Common Chord, Secant, Cyclic Quadrilateral, Concurrent Lines, Concyclic and Collinear Points.

Geometry Problem 1495

Geometry Problem 1495.
Circle, Parallel Chords, 30 Degree Angle, Radius Squared.

Geometry Problem 1485

Geometry Problem 1485.
Triangle, Orthocenter, Altitude, Circle, Diameter, Tangent, Measurement.

Dynamic Geometry 1479

Dynamic Geometry 1479.
Triangle, Circumcircle, Angle Bisector, Perpendicular Bisector, Chord, Concyclic Points, Parallel Lines,, Step-by-step Illustration. GeoGebra, iPad.

Dynamic Geometry 1474

Dynamic Geometry 1474.
Butterfly Theorem, Circle, Chords, Midpoints, Step-by-step Illustration.

Geometry Problem 1453

Geometry Problem 1453.
Two Semicircles, Cyclic Quadrilateral, Concyclic Points, iPad.

Dynamic Geometry 1449

Dynamic Geometry 1449.
Salmon Line. Step-by-step illustration using GeoGebra.

Problem 1439

Geometry Problem 1439.
Rectangle, Diagonal, Perpendicular, Circles, Areas, Art, Poster, Typography, iPad Apps.

Problem 1435

Geometry Problem 1435.
Circle, Diameter, Inscribed Circles, Circular Sector, Parallelogram, Parallel Lines, Tangency Points, Poster, Typography, iPad Apps.

Problem 1431

Geometry Problem 1431.
Triangle, Circumcircle, Parallel Chord, Apollonius, LLC, Congruent Angles, Poster, Conformal Mapping.

Problem 1402

Geometry Problem 1402.
Triangle, Three Tangent Circles, Parallel Diameter, Collinear Points.

Problem 1401

Geometry Problem 1401.
Right Triangle with three circles on the sides, Isosceles, Diameter, Center, Tangent, Congruence.

Problem 1397

Geometry Problem 1397.
Circle, Diameter, Tangent, Secant, 90 Degrees Angle, Perpendicular, Collinear Points.

Problem 1382 Circle, Diameter, Radius, Perpendicular, Congruence

Geometry Problem 1382.
Circle, Diameter, Radius, Perpendicular, Congruence.

Problem 1380 Circles, Tangents, Chords

Geometry Problem 1380.
Common Internal Tangents. Circles, Secant, Congruent Chords.

Problem 1379 Circles, Tangents, Chords

Geometry Problem 1379.
Common External Tangents. Circles, Secant, Congruent Chords.

Geometry problem 1365

Geometry Problem 1365.
Circle, Tangent, Secant, Chord, Parallel, Midpoint, Sketch, iPad Apps.

Geometry problem 1355

Geometry Problem 1355.
Triangle, Midpoint, Median, Circle, Chord, Equal Product of measure of segments.

Geometry problem 1354

Geometry Problem 1354.
Circle, Tangent Lines, Secant, Chord, Center, Parallel Lines.

Geometry problem 1353

Geometry Problem 1353.
Tangent Circles, Perpendicular Diameters, Congruence, 30 Degrees.

Geometry problem 1343

Problem 1343.
Triangle, Excircles, Circle, Tangent, Tangency Points, Chord, Perpendicular, 90 Degrees, Collinearity. Machu Picchu in the background.

Geometry problem 1342

Problem 1342.
Circle, Secant, Chord, Midpoint, Concyclic Points, Cyclic Quadrilateral.

Geometry problem 1321

Geometry Problem 1321.
Intersecting Circles, Diameter, Secant, Chord, Collinearity.

Geometry problem 1281

Geometry Problem 1281.
Triangle, Circle, Diameter, Tangent, Altitude, Congruent Angles.

Geometry problem 1261

Geometry Problem 1261.
Cyclic Quadrilateral, Circle, Diameter, Midpoint, Measurement.

Geometry problem 1259

Geometry Problem 1259.
Triangle, Circumcircle, Circle, Diameter, Parallel Lines.

Geometry problem 1251

Geometry Problem 1251.
Triangle, Circle, Diameter, Perpendicular, 90 Degrees.

Geometry problem 1250

Geometry Problem 1250.
Cyclic or Inscribed Quadrilateral, Circle, Diameter, Congruence.

Geometry problem 1191

Geometry Problem 1191
Circle, Chords, Diameter, Congruence, Midpoint, Collinearity, Bisector.

Geometry problem 1190

Geometry Problem 1190
Circle, Chords. Congruence.

Geometry problem 1181

Geometry Problem 1181
Cyclic Quadrilateral and Tangential Quadrilateral, Diameter as a Diagonal, Incenter, Circumcenter.

Geometry problem 1151

Geometry Problem 1151.
Circle, Diameter, Chord, Perpendicular, 90 Degrees, Metric Relations.

Geometry Problem 1090

Geometry Problem 1090.
Circle, Diameters, Chord, Perpendicular, Metric Relations.

Geometry Problem 1084

Geometry Problem 1084.
Circle, Chord, Radius, Diameter, Parallel lines, 45 Degrees, Metric Relations.

Geometry Problem 1083

Geometry Problem 1083.
Semicircle, Diameter, Perpendicular, 90 Degrees, Tangent Line, Metric Relations.

Geometry Problem 1071

Geometry Problem 1071.
Arbelos, Semicircles, Diameter, Circle, Perpendicular, Common Tangent, Parallel, Collinear Points, 90 Degrees, Midpoint.

Geometry Problem 1070

Geometry Problem 1070.
Circle, Chord, Equilateral Triangle, Square, Rectangle, Area, Diameter, Perpendicular.

Geometry Problem 1058

Geometry Problem 1058.
Triangle, Sum of the Areas, Altitude, Perpendicular, Circumcircle, Circle, Diameter.

Geometry Problem 1057

Geometry Problem 1057.
Triangle, Area, Circle with Perpendicular Diameters, Tangent, Secant.

Geometry Problem 1048

Geometry Problem 1048.
Circles, Tangent, Perpendicular, Diameter, Angle Bisector.

Geometry Problem 1033

Geometry Problem 1033.
Triangle, Angle Obtuse, Circumcircle, Diameter, Area.

Geometry Problem 1019

Geometry Problem 1019.
Circle, Diameter, Perpendicular, Chord, Tangent, Sum.

Geometry Problem 951

Geometry Problem 951.
Intersecting Circles, Chord, Diameter, Parallel, Cyclic Quadrilateral, Concyclic Points.

Triangle, Orthocenter, Circumcircle, Diameter, Midpoint

Geometry Problem 783
Triangle, Orthocenter, Circumcenter, Circumcircle, Diameter, Altitude, Midpoint.

Triangle, Orthocenter, Circumcircle, Diameter, Altitude, Parallelogram

Geometry Problem 782
Triangle, Orthocenter, Circumcenter, Circumcircle, Diameter, Altitude, Parallelogram.

Triangle, Distance from the Orthocenter to a Vertex, Circle, Circumradius, Side, Square.

Geometry Problem 778
Triangle, Distance from the Orthocenter to a Vertex, Circle, Circumradius, Side, Square.

Isosceles Triangle, Circle, Diameter, Altitude, Chord

Geometry Problem 760
Isosceles Triangle, Circle, Diameter, Altitude, Chord, Metric relations.

Tangent Circles, Incenter, Chord

Geometry Problem 713.
Tangent Circles, Diameter, Chord, Tangent, Incenter, Incircle, Triangle.

Semicircles, Tangent, Perpendicular, Angle

Geometry Problem 712.
Semicircle, Diameter, Tangent, Perpendicular, Angle Measure.

Circle, Area, Tangent, Intersecting, Lune

Geometry Problem 708.
Circle, Tangent, Intersecting, Lune, Area, Diameter.

Intersecting Circles, Diameter

Geometry Problem 705.
Intersecting Circles, Diameter, Angles, Measurement.

Intersecting Circles, Diameter, Perpendicular

Geometry Problem 701.
Intersecting Circles, Diameter, Perpendicular, Angles, Congruence.

Concentric Circles

Geometry Problem 680.
Concentric Circles, Radii, Chords, Perpendicular, Metric Relations.

Circles, Diameter, Tangent, Metric Relations

Geometry Problem 676.
Circles, Diameter, Tangent, Chord, Metric Relations.

Tangent Circles, Geometric Mean

Geometry Problem 672.
Internally tangent circles, Chord, Tangent, Geometric Mean.

Triangle, Altitudes, Circles, Angles

Geometry Problem 658.
Triangle, Altitudes, Diameter, Circle, Angles.

Online Math: Geometry Problem 571, Circle

Problem 571.
Circle, Diameter, Chord, Perpendicular, Measurement.

Cyclic quadrilateral, Diagonal, Diameter

Problem 530.
Cyclic Quadrilateral, Diagonal, Diameter, Chord, Perpendicular, Congruence.

Right Trapezoid, Circle, Diameter

Problem 529.
Right Trapezoid, Circle, Diameter, Chord.

Circle, Tangent, Diameter, Radius, Congruence

Problem 525.
Circles, Diameter, Chord, Tangent, Radius, Congruence, Measurement.

Tangent Circles

Problem 523.
Tangent Circles, Diameter, Chord, Perpendicular, Collinearity.

Geometry Problem: Right triangle, Circle, Tangent

Problem 522.
Right Triangle, Circle, Diameter, Chord, Tangent.

Circle, Diameter, Chord, Perpendicular

Problem 500.
Circle, Diameter, Chord, Perpendicular, Measure.

Circle, Area, 90 Degrees

Problem 487.
Intersecting Circles, Area, Diameter and Chord, Parallel, 90 Degrees.

 Triangle, circle, angle, altitude

Problem 480.
Triangle, Circle, Center, Diameter, Chord, Altitude, Angle, Circumcenter.

Triangle, Sides, Circumradius

Problem 478.
Triangle, Sides, Circumradius, Circumcenter, Circumcircle, Diameter, Chord.

Three tangent circles

Proposed Problem 456.
Three tangent circles, Center, Chord, Secant, Collinear, Diameters and Chords.

Tangent circles, diameter

Proposed Problem 448.
Tangent Circles, Diameter, Perpendicular, Chord.

Tangent Circles, Chords, Perpendiculars

Proposed Problem 438.
Tangent Circles, Diameter, Chord, Perpendicular, Congruence, Measurement, Parallel lines.

Tangent Circles, Chords, Perpendiculars

Proposed Problem 437.
Tangent Circles, Diameter, Chord, Perpendicular, Congruence, Measurement.

Tangent Circles, Chords, Perpendiculars

Proposed Problem 436.
Tangent Circles, Diameter, Chord, Perpendicular, Congruence, Measurement.

Problem about square and inscribed circle

Proposed Problem 373.
Square, Inscribed Circle, Diagonal, Perpendicular, Angle, Diameters and Chords.

Triangle area, Circle, Curvilinear triangle

Proposed Problem 364.
Obtuse triangle, Congruence, Circles, Diameter, Chord, Curvilinear triangle, Area.

Circle and Inscribed Semicircle

Proposed Problem 333.
Circle inscribed in a semicircle, Perpendicular to the common tangent, Diameters and Chords.

Triangle, Altitudes, Concyclic Points

Proposed Problem 329.
Triangle, Altitudes, Circle, Diameter, Concyclic points, Diameters and Chords.

Circle inscribed in a semicircle

Proposed Problem 310.
Circle Inscribed in a Semicircle, 45 Degrees Angle, Diameters and Chords.

Right Triangle Circumcenter, Excenter

Proposed Problem 294.
Right triangle, Circumcenter, Excenter, Hypotenuse, Perpendicular, Diameters and Chords.

Cube of the external common tangent

Proposed Problem 272.
Tangent Circles, the Cube of the Common external tangent, Diameters and Chords.

Cube of the external common tangent

Proposed Problem 271.
Tangent Circles, the Cube of the Common external tangent, Diameters and Chords.

Elearning 190 tangent circles, chord, perpendicular

Proposed Problem 190. Tangent circles, Tangent chord, Perpendicular, Distance, Intersection of a Line with a Circle, Diameter.

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Last updated: Feb 18, 2024