Online Geometry: Circles, Theorems and Problems

Circles, Theorems and Problems: Table of Content (Page 1 of 10)

Circle definition.

Chord. Index.
A chord of a circle is the line segment joining two points on the circle. 

Diameters and Chords, Theorems and Problems. Index.

Semicircle Definition.

Semicircle. Index.
Theorems and Problems.

Circular Sector. Index.
Theorems and Problems. 

Circular Segment. Index.
Theorems and Problems. 

Concentric Circles. Index.
Theorems and Problems. 

Intersecting Circles Index.
Theorems and Problems.

Tangent Circles Index
 

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

Circumcircle Index.

Cyclic Quadrilateral.
 

Concyclic Points.
 

Lunes of Hippocrates
 

Billiards and Geometry - Index
Billiards Ball.

The Geometry of Sprawl: Sun City, AZ, Geometric Sociology - Map and News.

Word Cloud of Circle.
Visual Summary.

Circumcenter. Index.

Incenter of a triangle. Index.

Excenter. Index.
Excircle, Exradius.

Soddy Circles and Descartes Theorem.
Three tangent circles, Inscribed and Circumscribed Circles, Radii.

Mascheroni construction with compass alone. Index

Ptolemy's Theorems and Problems - Index.

Brahmagupta Theorem and Problems - Index
Brahmagupta (598–668) was an Indian mathematician and astronomer who discovered a neat formula for the area of a cyclic quadrilateral.

Tangential or Circumscribed Quadrilateral
 

Mascheroni construction: Find the center of a circle with compass alone.

Mascheroni construction: Construct the circumcircle of a triangle with compass alone.

Study: Walking in circles.
Max-Planck-scientists show that people really walk in circles when lost.

Euclid's Elements Book I, Proposition 3: Given two unequal straight lines, to cut off from the greater a straight line equal to the less

Euclid's Elements Book I, Proposition 2: To place at a given point (as an extremity) a straight line equal to a given straight line

Euclid's Elements Book I, Proposition 1: On a given finite line to construct an equilateral triangle

Distance between the Incenter and the Centroid of a Triangle.
Formula in terms of the sides a,b,c.

Distances between Triangle Centers Index.

Tangential or Circumscribed Quadrilateral: Diagonals, Inradii Theorem.

Six Tangential or Circumscribed Quadrilaterals Theorem.

Tangential or Circumscribed Quadrilateral: Pitot Theorem.

Geometry Problem 724.
Circumscribed Quadrilateral, Circle, Angle, Incenter, Half the Measure.

Geometry Problem 723.
Squares, Circumscribed Circles, Collinear points.

Geometry Problem 722.
Squares, Circumscribed Circles, Collinear points.

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

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

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

Geometry Problem 707.
Triangle, Excenters, Angle Bisectors, Angle, Measurement.

Geometry Problem 706.
Triangle, Cevian, Three Circumcenters, Circumcircles, Concyclic Points, Cyclic quadrilateral.

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

Geometry Problem 703.
Triangle, Incircle, Tangency point, Diameter, Congruence.

Geometry Problem 702.
Triangle, Circumcircle, Parallel, Concyclic Points.

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

Geometry Problem 700.
Equilateral Triangle, Circle, Circular Segment, Midpoint of a side, Metric Relations.

Geometry Problem 699.
Equilateral Triangle, Circle, Circular Segment, Midpoint, Metric Relations.

Geometry Problem 697.
Square, Circle, Sector, Segment, Tangent, Inscribed, Congruence, Mind Map, Polya.

Geometry Problem 693.
Square, Inscribed and Circumscribed Circle, Areas, Mind Map, Polya.

Geometry Problem 692.
Quatrefoil, Four Equal Circles and a Circle Inscribed in a Square, Areas, Mind Map, Polya.

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

Geometry Problem 679.
Triangle, Circle, Median, Proportion.

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

Geometry Problem 675.
Intersecting Circles, Secant, 45 and 90 Degrees, Collinear Points.

Geometry Problem 673.
Internally tangent circles, Chord, Tangent, Metric Relations.

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

Geometry Problem 669.
Triangle, Circumcircle, Incenter, Midpoint, Collinear points, Mind Map.

Geometry Problem 668.
Right triangle, Incircles, Parallel, Common Tangent, Mind Map.

Geometry Problem 667.
Intersecting Circles, Secant, Tangent, Metric Relations, Mind Map.

Geometry Problem 666.
Intersecting Circles, Secant, Tangent, Concyclic points, Mind Map.

Geometry Problem 665.
Intersecting Circles, Secant, Tangent, Angles, Mind Map.

Geometry Problem 664.
Triangle, 60 Degrees, Orthocenter, Incenter, Circumcenter, Angles, Triangle centers.

Geometry Problem 662.
Triangle, Incenter, Circumcenter, Orthocenter, Circle, Angle, Measurement.

Geometry Problem 661.
Intersecting Circles, Centers, Secant, Parallelogram.

Geometry Problem 660.
Triangle, Circle, Diameter, Perpendicular Lines.

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

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

Geometry Problem 653.
Archimedes Book of Lemmas: Proposition 13
Circle, Chord, Perpendicular, Congruence.

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

Geometry Problem 651.
Archimedes Book of Lemmas: Proposition 11
Perpendicular chords, Arcs, Radius.

Geometry Problem 650.
Tangent Circles, Diameter, Radius, Chord, Perpendicular.

Geometry Problem 649.
Archimedes Book of Lemmas: Proposition 10
Tangent, Chord, Parallel, Midpoint.

Geometry Problem 648.
Archimedes Book of Lemmas: Proposition 9
Perpendicular chords, Arcs.

Geometry Problem 647.
Archimedes Book of Lemmas: Proposition 8
Angle trisection. Neusis construction.

Geometry Problem 646.
Archimedes Book of Lemmas: Proposition 7
Square,Inscribed and Circumscribed Circles, Area.

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

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 628
Cyclic Quadrilateral, Congruence, Parallel Lines.

Geometry Problem 627
Cyclic Quadrilateral, Congruence, Concyclic Points.

Geometry Problem 626
Triangle, Distance from the Incenter to an Excenter.

Geometry Problem 624
Triangle, Incenter, Excenter, Incircle, Excircle, Similarity.

Geometry Problem 623
Triangle, Incenter, Excenter, Incircle, Excircle, Concyclic Points.

Geometry Problem 622
Square with Perpendiculars, Transversal, Congruence.

Geometry Problem 610
Intersecting Circles, Radius, Parallel, Common Tangent, Angle, 90 Degrees.

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