Geometry Problems, Online Education

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

Semicircle, Theorems and Problems - Index

Online education degree: online geometry classes

Semicircle definition

Semicircle Definition.

Arbelos, Theorems and Problems Index

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

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

Geometry problem 1335

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

Geometry problem 1301

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

Geometry problem 1300

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

Geometry problem 1298

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

Geometry problem 1297

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

Geometry problem 1168

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

Geometry Problem 1071

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

Geometry Problem 989

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

Problem 936

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

Problem 927

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

Semicircle, Chord, Arc, Area

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

Semicircle, Chord, Arc, Area

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

Triangle, Incircle, Arbelos, Area

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

Circle Area, Tangent 

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

Parallelogram, Perpendicular, Semicircle, Area

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

Right Triangle Area, Incircle, Semicircle

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

Circle, Chord, Congruence, 90 Degrees

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

Parallelogram, Circle, Chord

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

Cyclic quadrilateral, tangent, perpendicular

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

Semicircles, Tangent, Perpendicular, Angle

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

Archimedes Book of Lemmas Proposition 14

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

Archimedes Book of Lemmas Proposition 12

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

Archimedes Book of Lemmas Proposition 6

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

Archimedes Book of Lemmas Proposition 5

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

Archimedes Book of Lemmas Proposition 4

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

Archimedes Book of Lemmas Proposition 3

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

Archimedes Book of Lemmas Proposition 2

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

Semicircle, Perpendicular, Inscribed Circle, Tangent, Congruence

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

Arbelos, Circle, Concyclic Points

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

Semicircle, Perpendicular, Inscribed Circle, Tangent, Chord

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

Semicircle, Perpendicular, Inscribed Circle, Tangent

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

Semicircle, Perpendicular, Inscribed Circle, Radius

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

Circle Area, Tangent

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

Online Math: Geometry Problem 571, Circle

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

Right Trapezoid, Circle, Diameter

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

Circle, Tangent, Diameter, Radius, Congruence

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

Tangent Circles

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

Geometry Problem: Right triangle, Circle, Tangent

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

Circle, Diameter, Chord, Perpendicular

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

Elearn 494: Circular Sector, 90 Degrees

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

Elearn 493: Right triangle, Circumcircle, Perpendicular

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

Circle, Area, 90 Degrees

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

Square, Circle, Tangent

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

Three tangent circles

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

Tangent circles, diameter

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

Tangent Circles, Chords, Perpendiculars

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

Tangent Circles, Chords, Perpendiculars

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

Tangent Circles, Chords, Perpendiculars

Proposed Problem 436.
Tangent Circles, Diameter, Semicircles, 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.

Area of Triangle, Circles, Diameters

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

Circle and Inscribed Semicircle

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

Triangle, Altitudes, Concyclic Points

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

Right triangle Area, Semicircle, Square

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

Equilateral triangle and semicircle

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

Circle, Semicircle, Chord, Diameter

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

Circle inscribed in a semicircle

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

Archimedes Twin, Harmonic mean

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

Right Triangle Circumcenter, Excenter

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

Geometry Expressions

Geometry Expressions
Arbelos, Circle, Semicircles.

Tangent Circles, Harmonic Mean

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

Cube of the external common tangent

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

Cube of the external common tangent

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

Circle area and Pythagoras

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

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Last updated: May 7, 2017