|
|
Online Geometry: Semicircle and Diameter, Theorems and Problems. Level: Mathematics Education, High School, College
|
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 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 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.
|
|
|
|
|
|
|
|