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![Geometry Problems, Online Education](../geometry/h_online_math_geometry_910.jpg)
Online Geometry: Semicircle and Diameter, Theorems and Problems. Level: Mathematics Education, High School, College
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Semicircle, Theorems and Problems - Index
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![Online education degree: online geometry classes](semicircle_theorems_prob_1.jpg) |
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![Semicircle definition](../math_geometry_online_courses/semicircle_definition_1.jpg) |
Semicircle
Definition.
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![Arbelos, Theorems and Problems Index](../math_geometry_online_courses/arbelos_index_1.jpg)
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Arbelos, Theorems and Problems
Three tangent semicircles with collinear
centers.
Index |
![](../geometry/lune_hippocrates_index_1.jpg) |
Lune of Hippocrates Index
Semircles, Diameter, Right Triangle, Areas |
![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 1361](../school-college/4/p1361-two-nine-point-circle-angle-tutor-sketch-sw-1.jpg) |
Geometry Problem 1361.
Triangle, Two Nine-Point Circles, Feuerbach's Circle, Euler's Circle, Congruent Angles, Sketch, iPad Apps. |
![Geometry problem 1360](../school-college/4/p1360-nine-point-circle-euler-cyclic-tutor-sketch-sw-1.jpg) |
Geometry Problem 1360.
Triangle, Nine-Point Circle, Feuerbach's Circle, Euler's Circle, Cyclic Quadrilateral, Concyclic Points, Sketch, iPad Apps. |
![Geometry problem 1335](../school-college/4/p1335-squaring-circle-kite-lune-1.jpg) |
Problem 1335. The
Lune of Hippocrates has the same area of a Kite.
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![Geometry problem 1301](../school-college/4/p1301-arbelos-incircle-square-midpoint-1.jpg) |
Geometry Problem 1301.
Arbelos, Semicircles, Diameters, Circle, Incircle, Incenter, Square, Midpoint, Concurrency. |
![Geometry problem 1300](../school-college/3/p1300-arbelos-incircle-tangent-bisector-concurrency-1.jpg) |
Geometry Problem 1300.
Arbelos, Semicircles, Diameters, Circle, Incircle, Tangent, Perpendicular, Concurrent Lines. |
![Geometry problem 1298](../school-college/3/p1298-arbelos-incircle-angle-bisector-perpendicular-midpoint-1.jpg) |
Geometry Problem 1298.
Arbelos, Semicircles, Diameters, Circle, Incircle, Tangent, Angle Bisector, Perpendicular, Midpoint. |
![Geometry problem 1297](../school-college/3/p1297-arbelos-incircle-tangent-angle-bisector-1.jpg) |
Geometry Problem 1297.
Arbelos, Semicircles, Diameters, Circle, Incircle, Tangent, Angle Bisector. |
![Geometry problem 1168](../school-college/2/p1168-arbelos-construction-inscribed-circle-triangle-proof-tutor-1.jpg) |
Geometry Problem 1168
Construction of the Inscribed Circle of the Arbelos, Semicircles, Diameter, Circle, Triangle, Circumcircle, Tangent. |
![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 989](../school-college/p989-semicircle-arbelo-perpendicular-tangent-rectangle-midpoint-arc-1.jpg) |
Geometry Problem 989.
Arbelos, Semicircles, Diameter, Perpendicular, 90 Degree, Common External Tangent, Rectangle, Midpoint of Arc. |
![Problem 936](../school-college/p936-semicircle-diameter-circle-tangent-radius-metric-relations-1.jpg) |
Geometry Problem 936.
Circle, Semicircle, Diameter, Tangent, Radius, Chord, Metric Relations.
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![Problem 927](../school-college/p927-semicircle-equal-arcs-radius-chord-congruence-1.jpg) |
Geometry Problem 927.
Semicircle, Diameter, Radius, Equal Arcs, Chord, Congruence.
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![Semicircle, Chord, Arc, Area](../school-college/p825-semicircle-triangle-area-diameter-chord-arc-midpoint-sector-1.jpg) |
Geometry Problem 825.
Circle, Semicircle, Arc, Chord, Midpoint, Sector, Triangle, Area. |
![Semicircle, Chord, Arc, Area](../school-college/p822-circle-triangle-area-diameter-chord-midpoint-sector-1.jpg) |
Geometry Problem 822.
Circle, Semicircle, Arc, Chord, Midpoint, Sector, Triangle, Area. |
![Triangle, Incircle, Arbelos, Area](../school-college/p815-triangle-incircle-semicircle-tangent-arbelos-area-1.jpg) |
Geometry Problem
815.
Triangle, Incircle, Semicircles, Arbelos, Area. |
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Geometry Problem
812.
Four Tangent Circles, Semicircle, Common Tangent Line, Diameter, Area, Collinear Centers. |
![Parallelogram, Perpendicular, Semicircle, Area](../school-college/p808-parallelogram-perpendicular-right-triangle-semicircle-area-1.jpg) |
Geometry Problem 808
Parallelogram, Perpendicular, Right Triangle, Semicircle Area, Diameter. |
![Right Triangle Area, Incircle, Semicircle](../school-college/p807-right-triangle-area-semicircle-incircle-1.jpg) |
Geometry Problem 807
Right Triangle Area, Incircle, Tangency Points, Semicircle Area. |
![Circle, Chord, Congruence, 90 Degrees](../problem/p745-circle-chord-congruence-90-degrees-1.jpg) |
Geometry Problem
745.
Circle, 90 Degrees, Chord, Congruence, Perpendicular, Metric Relations. |
![Parallelogram, Circle, Chord](../problem/p744-parallelogram-circle-diameter-chord-congruence-1.jpg) |
Geometry Problem
744.
Parallelogram, Circle, Diameter, Chord, Congruence, Triangle, Metric Relations. |
![Cyclic quadrilateral, tangent, perpendicular](../problem/p737_cyclic_quadrilateral_1.jpg) |
Geometry Problem
737.
Cyclic Quadrilateral, Circumscribed Circle, Diameter, Tangent, Perpendicular. |
![Semicircles, Tangent, Perpendicular, Angle](../problem/p712_tangent_circles_1.jpg) |
Geometry Problem
712.
Semicircle, Diameter, Tangent, Perpendicular, Angle Measure. |
![Archimedes Book of Lemmas Proposition 14](../problem/p654_archimedes_lemma_14_1.jpg) |
Geometry Problem 654.
Archimedes Book of Lemmas: Proposition 14
Salinon, Semicircles, Diameter, Circle, Area. |
![Archimedes Book of Lemmas Proposition 12](../problem/p652_archimedes_lemma_12_1.jpg) |
Geometry Problem 652.
Archimedes Book of Lemmas: Proposition 12
Semicircle,
Perpendicular chords, Arcs, Radius. |
![Archimedes Book of Lemmas Proposition 6](../problem/p645_archimedes_lemma_06_1.jpg) |
Geometry Problem 645.
Archimedes Book of Lemmas: Proposition 6
Semicircle, Circle, Perpendicular, Arbelos, Inscribed Circle. |
![Archimedes Book of Lemmas Proposition 5](../problem/p644_archimedes_lemma_05_1.jpg) |
Geometry Problem 644.
Archimedes Book of Lemmas: Proposition 5
Semicircle, Circle, Perpendicular, Arbelos, Archimedean
Twins. |
![Archimedes Book of Lemmas Proposition 4](../problem/p643_archimedes_lemma_04_1.jpg) |
Geometry Problem 643.
Archimedes Book of Lemmas: Proposition 4
Semicircle, Circle, Perpendicular, Arbelos, Area. |
![Archimedes Book of Lemmas Proposition 3](../problem/p642_archimedes_lemma_03_1.jpg) |
Geometry Problem 642.
Archimedes Book of Lemmas: Proposition 3
Semicircle, Perpendicular, Arc, Midpoint, Congruence. |
![Archimedes Book of Lemmas Proposition 2](../problem/p641_archimedes_lemma_02_1.jpg) |
Geometry Problem 641.
Archimedes Book of Lemmas: Proposition 2
Semicircle, Tangent, Perpendicular, Midpoint. |
![Semicircle, Perpendicular, Inscribed Circle, Tangent, Congruence](../problem/p639_arbelos_circle_1.jpg) |
Geometry Problem 639
Semicircle, Diameter, Perpendicular, Inscribed Circle, Tangent, Arbelos, Congruence. |
![Arbelos, Circle, Concyclic Points](../problem/p638_arbelos_circle_1.jpg) |
Geometry Problem 638
Arbelos and Inscribed Circle,
Semicircle, Concyclic Points. |
![Semicircle, Perpendicular, Inscribed Circle, Tangent, Chord](../problem/p637_arbelos_circle_1.jpg) |
Geometry Problem 637
Semicircle, Diameter, Perpendicular, Inscribed Circle, Chord, Tangent, Arbelos. |
![Semicircle, Perpendicular, Inscribed Circle, Tangent](../problem/p636_tangent_circle_1.jpg) |
Geometry Problem 636
Semicircle, Diameter, Perpendicular, Inscribed Circle, Common Tangent. |
![Semicircle, Perpendicular, Inscribed Circle, Radius](../problem/p635_circle_radius_1.jpg) |
Geometry Problem 635
Semicircle, Diameter, Perpendicular, Inscribed Circle, Radius. |
![Circle Area, Tangent](../problem/p600_circle_area_1.jpg) |
Geometry Problem
600
Circle, Area, Tangent, Semicircle, Tangency Point. |
![Online Math: Geometry Problem 571, Circle](../problem/p571_circle_diameter_1.jpg) |
Problem
571.
Circle, Diameter, Chord, Semicircles, Perpendicular, Measurement. |
![Right Trapezoid, Circle, Diameter](../problem/p529_trapezoid_circle_1.jpg) |
Problem 529.
Right Trapezoid, Circle, Diameter, Semicircle. |
![Circle, Tangent, Diameter, Radius, Congruence](../problem/p525_circle_tangent.jpg) |
Problem 525.
Circles, Diameter, Semicircles, Tangent, Radius, Congruence, Measurement. |
![Tangent Circles](../problem/p523_tangent_circle_1.jpg) |
Problem 523.
Tangent Circles, Diameter, Semicircle, Perpendicular, Collinearity. |
![Geometry Problem: Right triangle, Circle, Tangent](../problem/p522_triangle_circle_1.jpg) |
Problem 522.
Right Triangle, Circle, Diameter, Semicircle, Tangent. |
![Circle, Diameter, Chord, Perpendicular](../problem/p500_circle_diameter_1.jpg) |
Problem
500.
Circle, Diameter, Semicircle, Chord, Perpendicular, Measure. |
![Elearn 494: Circular Sector, 90 Degrees](../problem/p494_circular_sector_1.jpg) |
Problem 494.
Circular Sector, 90 Degrees, Semicircle, Chord, Parallel. |
![Elearn 493: Right triangle, Circumcircle, Perpendicular](../problem/p493_triangle_circle_1.jpg) |
Problem 493.
Right Triangle, Circumcircle, Semicircle, Perpendicular, Chord. |
![Circle, Area, 90 Degrees](../problem/p487_circle_area_1.jpg) |
Problem 487.
Intersecting
Circles, Area, Diameter, Semicircle, Parallel, 90 Degrees. |
![Square, Circle, Tangent](../education/p458_triangle_circle_sector.jpg) |
Proposed
Problem 458.
Square, Semicircle, Circular Sector, Internal Common Tangent, Measurement. |
![Three tangent circles](../education/p456_tangent_circles_1.jpg) |
Proposed Problem 456.
Three tangent circles, Semicircles, Center, Chord, Secant, Collinear, Diameters and Chords. |
![Tangent circles, diameter](../problem/p448_tangent_circle_1.jpg) |
Proposed
Problem 448.
Tangent Circles, Semicircle, Diameter, Perpendicular, Chord. |
![Tangent Circles, Chords, Perpendiculars](../problem/p438_circle_chord_1.jpg) |
Proposed
Problem 438.
Tangent Circles, Semicircle, Diameter, Chord, Perpendicular, Congruence, Measurement,
Parallel lines. |
![Tangent Circles, Chords, Perpendiculars](../problem/p437_circle_chord_1.jpg) |
Proposed
Problem 437.
Tangent Circles, Diameter, Semicircle, Chord, Perpendicular, Congruence, Measurement. |
![Tangent Circles, Chords, Perpendiculars](../problem/p436_circle_chord_1.jpg) |
Proposed
Problem 436.
Tangent Circles, Diameter, Semicircles, 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. |
![Area of Triangle, Circles, Diameters](../problem/p360_area_triangle_17.jpg) |
Proposed
Problem 360.
Area of a triangle, Curvilinear triangles, Circles, Diameters,
Semicircles. |
![Circle and Inscribed Semicircle](../problem/p333_circle_semicircle_17.jpg) |
Proposed Problem
333.
Circle inscribed in a semicircle, Perpendicular to the common tangent. |
![Triangle, Altitudes, Concyclic Points](../problem/p329_triangle_altitude_17.jpg) |
Proposed Problem
329.
Triangle, Altitudes, Circle, Semicircle, Diameter, Concyclic points. |
![Right triangle Area, Semicircle, Square](../problem/p327_right_triangle_area_17.jpg) |
Proposed Problem
327.
Right triangle Area, Incircle, Circumcircle, Square. |
![Equilateral triangle and semicircle](../problem/p326_equilateral_triangle_1.jpg) |
Proposed Problem
326.
Equilateral triangle, Semicircle, Equal arcs. |
![Circle, Semicircle, Chord, Diameter](../problem/p311_circle_semicircle_17.jpg) |
Proposed Problem
311.
Circle Inscribed in a Semicircle, Chord, Diameter. |
![Circle inscribed in a semicircle](../problem/p310_circle_semicircle_17.jpg) |
Proposed Problem
310.
Circle Inscribed in a Semicircle, 45 Degrees Angle. |
![Archimedes Twin, Harmonic mean](../problem/p295_archimedes_twin_17.jpg) |
Proposed Problem 295.
Archimedean Twin Circles, Arbelos, Semicircles, Harmonic Mean, Radii, Perpendicular. |
![Right Triangle Circumcenter, Excenter](../problem/p294_triangle_excenter_17.jpg) |
Proposed Problem 294.
Right triangle, Circumcenter, Excenter, Hypotenuse, Perpendicular, Semicircle. |
![Geometry Expressions](../geometry/geometry_expressions_01a17.jpg) |
Geometry Expressions
Arbelos, Circle, Semicircles. |
![Tangent Circles, Harmonic Mean](../problem/p288_circles_harmonic_mean.jpg) |
Proposed Problem 288:
Tangent circles, Semicircle, Harmonic Mean, Radius, Diameter. |
![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,
Semicircles 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,
Semicircles, 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, Semicircle. |
![](../pythagoras/lunes_hippocrates_04_170.jpg) |
Lunes of Hippocrates 4
Semicircles, Right Triangle, Area. |
![](../pythagoras/lunes_hippocrates_03_170.jpg) |
Lunes of Hippocrates 3
Semicircles, Right Triangle, Area.
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![](../pythagoras/lunes_hippocrates_02_170.jpg) |
Lunes of Hippocrates 2
Semicircles, Right Triangle, Area. |
![](../pythagoras/lunes_hippocrates_01_170.jpg) |
Lunes of Hippocrates 1
Semicircles, Right Triangle, Area. |
![Circle area and Pythagoras](../problem/p099_circle_area_elearning_17.jpg) |
Problem 99: Circle Area, General Extension
to Pythagoras' Theorem.
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