Semicircle, Theorems and Problems - Index

Semicircle Definition.

Arbelos, Theorems and Problems
Three tangent semicircles with collinear centers.
Index 

Lune of Hippocrates Index
Semircles, Diameter, Right Triangle, Areas 

Geometry Problem 1602: Find the Distance from the Semicircle’s Center to the Incenter

Geometry Problem 1592: A Semicircle Challenge for Mental Clarity Involving Radii, Perpendiculars, Midpoint

Geometry Problem 1588: Unlocking the Tangent: Prove the Fifth of the Radius in a Sector with Semicircle.

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.
Triangle, Two Nine-Point Circles, Feuerbach's Circle, Euler's Circle, Congruent Angles, Sketch, iPad Apps.

Geometry Problem 1360.
Triangle, Nine-Point Circle, Feuerbach's Circle, Euler's Circle, Cyclic Quadrilateral, Concyclic Points, Sketch, iPad Apps.

Problem 1335. The Lune of Hippocrates has the same area of a Kite.

Geometry Problem 1301.
Arbelos, Semicircles, Diameters, Circle, Incircle, Incenter, Square, Midpoint, Concurrency.

Geometry Problem 1300.
Arbelos, Semicircles, Diameters, Circle, Incircle, Tangent, Perpendicular, Concurrent Lines.

Geometry Problem 1298.
Arbelos, Semicircles, Diameters, Circle, Incircle, Tangent, Angle Bisector, Perpendicular, Midpoint.

Geometry Problem 1297.
Arbelos, Semicircles, Diameters, Circle, Incircle, Tangent, Angle Bisector.

Geometry Problem 1168
Construction of the Inscribed Circle of the Arbelos, Semicircles, Diameter, Circle, Triangle, Circumcircle, Tangent.

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

Geometry Problem 989.
Arbelos, Semicircles, Diameter, Perpendicular, 90 Degree, Common External Tangent, Rectangle, Midpoint of Arc.

Geometry Problem 936.
Circle, Semicircle, Diameter, Tangent, Radius, Chord, Metric Relations.

Geometry Problem 927.
Semicircle, Diameter, Radius, Equal Arcs, Chord, Congruence.

Geometry Problem 825.
Circle, Semicircle, Arc, Chord, Midpoint, Sector, Triangle, Area.

Geometry Problem 822.
Circle, Semicircle, Arc, Chord, Midpoint, Sector, Triangle, Area.

Geometry Problem 815.
Triangle, Incircle, Semicircles, Arbelos, Area.

Geometry Problem 812.
Four Tangent Circles, Semicircle, Common Tangent Line, Diameter, Area, Collinear Centers.

Geometry Problem 808
Parallelogram, Perpendicular, Right Triangle, Semicircle Area, Diameter.

Geometry Problem 807
Right Triangle Area, Incircle, Tangency Points, Semicircle Area.

Geometry Problem 745.
Circle, 90 Degrees, Chord, Congruence, Perpendicular, Metric Relations.

Geometry Problem 744.
Parallelogram, Circle, Diameter, Chord, Congruence, Triangle, Metric Relations.

Geometry Problem 737.
Cyclic Quadrilateral, Circumscribed Circle, Diameter, Tangent, Perpendicular.

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

Geometry Problem 654.
Archimedes Book of Lemmas: Proposition 14
Salinon, Semicircles, Diameter, Circle, Area.

Geometry Problem 652.
Archimedes Book of Lemmas: Proposition 12
Semicircle, Perpendicular chords, Arcs, Radius.

Geometry Problem 645.
Archimedes Book of Lemmas: Proposition 6
Semicircle, Circle, Perpendicular, Arbelos, Inscribed Circle.

Geometry Problem 644.
Archimedes Book of Lemmas: Proposition 5
Semicircle, Circle, Perpendicular, Arbelos, Archimedean Twins.

Geometry Problem 643.
Archimedes Book of Lemmas: Proposition 4
Semicircle, Circle, Perpendicular, Arbelos, Area.

Geometry Problem 642.
Archimedes Book of Lemmas: Proposition 3
Semicircle, Perpendicular, Arc, Midpoint, Congruence.

Geometry Problem 641.
Archimedes Book of Lemmas: Proposition 2
Semicircle, Tangent, Perpendicular, Midpoint.

Geometry Problem 639
Semicircle, Diameter, Perpendicular, Inscribed Circle, Tangent, Arbelos, Congruence.

Geometry Problem 638
Arbelos and Inscribed Circle, Semicircle, Concyclic Points.

Geometry Problem 637
Semicircle, Diameter, Perpendicular, Inscribed Circle, Chord, Tangent, Arbelos.

Geometry Problem 636
Semicircle, Diameter, Perpendicular, Inscribed Circle, Common Tangent.

Geometry Problem 635
Semicircle, Diameter, Perpendicular, Inscribed Circle, Radius.

Geometry Problem 600
Circle, Area, Tangent, Semicircle, Tangency Point.

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

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

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

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

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

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

Problem 494.
Circular Sector, 90 Degrees, Semicircle, Chord, Parallel.

Problem 493.
Right Triangle, Circumcircle, Semicircle, Perpendicular, Chord.

Problem 487.
Intersecting Circles, Area, Diameter, Semicircle, Parallel, 90 Degrees.

Proposed Problem 458.
Square, Semicircle, Circular Sector, Internal Common Tangent, Measurement.

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

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

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

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

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

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

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

Proposed Problem 360.
Area of a triangle, Curvilinear triangles, Circles, Diameters, Semicircles.

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

Proposed Problem 329.
Triangle, Altitudes, Circle, Semicircle, Diameter, Concyclic points.

Proposed Problem 327.
Right triangle Area, Incircle, Circumcircle, Square.

Proposed Problem 326.
Equilateral triangle, Semicircle, Equal arcs.

Proposed Problem 311.
Circle Inscribed in a Semicircle, Chord, Diameter.

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

Proposed Problem 295.
Archimedean Twin Circles, Arbelos, Semicircles, Harmonic Mean, Radii, Perpendicular.

Proposed Problem 294.
Right triangle, Circumcenter, Excenter, Hypotenuse, Perpendicular, Semicircle.

Geometry Expressions
Arbelos, Circle, Semicircles.

Proposed Problem 288: Tangent circles, Semicircle, Harmonic Mean, Radius, Diameter.

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

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

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

Lunes of Hippocrates 4
Semicircles, Right Triangle, Area. 

Lunes of Hippocrates 3
Semicircles, Right Triangle, Area.
 

Lunes of Hippocrates 2
Semicircles, Right Triangle, Area. 

Lunes of Hippocrates 1
Semicircles, Right Triangle, Area. 

Problem 99: Circle Area, General Extension to Pythagoras' Theorem.