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Circles, Theorems and Problems: Table of Content
(Page 1 of 10)
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Circle definition.
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Chord.
Index.
A chord of a circle is the line segment joining two points on the
circle.
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Diameters and Chords,
Theorems and Problems.
Index.
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Semicircle
Definition.
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Semicircle.
Index.
Theorems and Problems.
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Circular
Sector.
Index.
Theorems and Problems.
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Circular Segment. Index.
Theorems and Problems.
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Concentric
Circles.
Index.
Theorems and Problems.
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Intersecting Circles Index.
Theorems and Problems. |
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Tangent Circles Index
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Arbelos, Theorems and Problems
Three tangent semicircles with collinear
centers.
Index |
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Circumcircle
Index.
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Cyclic Quadrilateral.
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Concyclic
Points.
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Lunes of Hippocrates
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Billiards and Geometry -
Index
Billiards Ball. |
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The Geometry of Sprawl: Sun City, AZ, Geometric Sociology - Map and News. |
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Word
Cloud of Circle.
Visual Summary. |
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Circumcenter.
Index.
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Incenter of a triangle.
Index.
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Excenter.
Index.
Excircle, Exradius.
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Soddy Circles and Descartes Theorem.
Three tangent circles,
Inscribed and Circumscribed Circles, Radii. |
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Mascheroni
construction with compass alone. Index
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Ptolemy's Theorems and Problems - Index. |
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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. |
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Tangential
or Circumscribed Quadrilateral
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Mascheroni construction: Find the center of a circle with compass alone.
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Mascheroni construction: Construct the circumcircle of
a triangle with compass alone.
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Study: Walking in circles.
Max-Planck-scientists show that people really walk in circles when lost.
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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 |
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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 |
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Euclid's Elements Book I, Proposition 1:
On a given finite line to construct an equilateral triangle |
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Distance between the Incenter and the Centroid of a Triangle.
Formula in terms of the sides a,b,c. |
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Distances between Triangle Centers
Index.
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Tangential or Circumscribed Quadrilateral:
Diagonals, Inradii Theorem. |
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Six Tangential or Circumscribed Quadrilaterals Theorem. |
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Tangential or Circumscribed Quadrilateral:
Pitot Theorem. |
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Geometry Problem
724.
Circumscribed Quadrilateral, Circle, Angle, Incenter, Half
the Measure. |
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Geometry Problem
723.
Squares, Circumscribed Circles, Collinear points. |
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Geometry Problem
722.
Squares, Circumscribed Circles, Collinear points. |
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Geometry Problem
713.
Tangent Circles, Diameter, Chord, Tangent, Incenter, Incircle, Triangle. |
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Geometry Problem
712.
Semicircle, Diameter, Tangent, Perpendicular, Angle Measure. |
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Geometry Problem
708.
Circle, Tangent, Intersecting, Lune, Area, Diameter. |
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Geometry Problem
707.
Triangle, Excenters, Angle Bisectors, Angle, Measurement. |
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Geometry Problem
706.
Triangle, Cevian, Three Circumcenters, Circumcircles, Concyclic Points, Cyclic quadrilateral. |
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Geometry Problem
705.
Intersecting Circles, Diameter, Angles, Measurement. |
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Geometry Problem
703.
Triangle, Incircle, Tangency point, Diameter, Congruence. |
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Geometry Problem
702.
Triangle, Circumcircle, Parallel, Concyclic Points. |
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Geometry Problem
701.
Intersecting Circles, Diameter, Perpendicular, Angles, Congruence. |
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Geometry Problem
700.
Equilateral Triangle, Circle, Circular Segment, Midpoint of
a side, Metric Relations. |
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Geometry Problem 699.
Equilateral Triangle, Circle, Circular Segment, Midpoint, Metric Relations. |
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Geometry Problem 697.
Square, Circle, Sector, Segment, Tangent, Inscribed, Congruence, Mind Map, Polya. |
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Geometry Problem 693.
Square, Inscribed and Circumscribed Circle, Areas, Mind Map, Polya. |
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Geometry Problem 692.
Quatrefoil, Four Equal Circles and a Circle Inscribed in a Square, Areas, Mind Map, Polya. |
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Geometry Problem 680.
Concentric Circles, Radii, Chords, Perpendicular, Metric Relations. |
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Geometry Problem 679.
Triangle, Circle, Median, Proportion. |
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Geometry Problem 676.
Circles, Diameter, Tangent, Chord, Metric Relations. |
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Geometry Problem 675.
Intersecting Circles, Secant, 45 and 90 Degrees, Collinear Points. |
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Geometry Problem 673.
Internally tangent circles, Chord, Tangent, Metric Relations. |
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Geometry Problem 672.
Internally tangent circles, Chord, Tangent, Geometric Mean. |
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Geometry Problem 669.
Triangle, Circumcircle, Incenter, Midpoint, Collinear points, Mind Map. |
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Geometry Problem 668.
Right triangle, Incircles, Parallel, Common Tangent, Mind Map. |
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Geometry Problem 667.
Intersecting Circles, Secant, Tangent, Metric Relations, Mind Map. |
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Geometry Problem 666.
Intersecting Circles, Secant, Tangent, Concyclic points, Mind Map. |
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Geometry Problem 665.
Intersecting Circles, Secant, Tangent, Angles, Mind Map. |
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Geometry Problem 664.
Triangle, 60 Degrees, Orthocenter, Incenter, Circumcenter, Angles,
Triangle centers. |
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Geometry Problem 662.
Triangle, Incenter, Circumcenter, Orthocenter, Circle, Angle, Measurement. |
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Geometry Problem 661.
Intersecting Circles, Centers, Secant, Parallelogram. |
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Geometry Problem 660.
Triangle, Circle, Diameter, Perpendicular Lines. |
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Geometry Problem 658.
Triangle, Altitudes, Diameter, Circle, Angles. |
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Geometry Problem 654.
Archimedes Book of Lemmas: Proposition 14
Salinon, Semicircles, Diameter, Circle, Area. |
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Geometry Problem 653.
Archimedes Book of Lemmas: Proposition 13
Circle, Chord, Perpendicular, Congruence. |
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Geometry Problem 652.
Archimedes Book of Lemmas: Proposition 12
Perpendicular chords, Arcs, Radius. |
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Geometry Problem 651.
Archimedes Book of Lemmas: Proposition 11
Perpendicular chords, Arcs, Radius. |
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Geometry Problem 650.
Tangent Circles, Diameter, Radius, Chord, Perpendicular. |
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Geometry Problem 649.
Archimedes Book of Lemmas: Proposition 10
Tangent, Chord, Parallel, Midpoint. |
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Geometry Problem 648.
Archimedes Book of Lemmas: Proposition 9
Perpendicular chords, Arcs. |
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Geometry Problem 647.
Archimedes Book of Lemmas: Proposition 8
Angle trisection. Neusis construction. |
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Geometry Problem 646.
Archimedes Book of Lemmas: Proposition 7
Square,Inscribed and Circumscribed Circles, Area. |
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Geometry Problem 639
Semicircle, Diameter, Perpendicular, Inscribed Circle, Tangent, Arbelos, Congruence. |
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Geometry Problem 637
Semicircle, Diameter, Perpendicular, Inscribed Circle, Chord, Tangent, Arbelos. |
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Geometry Problem 636
Semicircle, Diameter, Perpendicular, Inscribed Circle, Common Tangent. |
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Geometry Problem 635
Semicircle, Diameter, Perpendicular, Inscribed Circle, Radius. |
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Geometry Problem 628
Cyclic Quadrilateral, Congruence, Parallel Lines. |
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Geometry Problem 627
Cyclic Quadrilateral, Congruence, Concyclic Points. |
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Geometry Problem 626
Triangle, Distance from the Incenter to an Excenter. |
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Geometry Problem 624
Triangle, Incenter, Excenter, Incircle, Excircle, Similarity. |
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Geometry Problem 623
Triangle, Incenter, Excenter, Incircle, Excircle, Concyclic Points. |
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Geometry Problem 622
Square with Perpendiculars, Transversal, Congruence. |
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Geometry Problem
610
Intersecting Circles, Radius, Parallel, Common Tangent, Angle, 90 Degrees. |
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