Circles, Theorems and Problems: Table of Content (Page 1 of 5)

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

Circular Sector. Index.
Theorems and Problems. 

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

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

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

Intersecting Circles Index.
Theorems and Problems.

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

Tangent Circles Index
 

Cyclic Quadrilateral.
 

Tangential or Circumscribed Quadrilateral
 

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

Tangential or Circumscribed Quadrilateral: Diagonals, Inradii Theorem.

Six Tangential or Circumscribed Quadrilaterals Theorem.

Tangential or Circumscribed Quadrilateral: Pitot Theorem.

Proposed Problem 418.
Triangle, Incircle, Inradius, Equal Tangent circles, Radius.

Proposed Problem 417.
Tangent circles, Tangent lines, Angles.

Proposed Problem 413.
Cyclic Quadrilateral, Orthocenter, Parallelogram, Concurrency, Congruence.

Proposed Problem 408.
Cyclic quadrilateral, Perpendicular, Parallelogram, Congruence.

Proposed Problem 407.
Circle, Angle, Tangent, Perpendicular, Secant, Radius, Center.

Proposed Problem 403.
Circular sector, 90 degrees, Circle, Semicircle, Area.

Proposed Problem 401.
Area, Triangle, Angle bisector, Circumcircle, Perpendicular bisector, Congruence.

Proposed Problem 400.
Triangle, Angle bisector, Circumcircle, Perpendicular, Congruence.

Proposed Problem 394.
Square, 90 Degree Arc, Diagonal, Congruence.

Proposed Problem 393.
Triangle, Orthocenter, Circumcircles, Congruence, Collinear.

Proposed Problem 380.
Triangle, Excenter, Parallel to a side, Angle, Congruence.

Proposed Problem 379.
Triangle, Excenter, Parallel to a side, Angle, Congruence.

Proposed Problem 378.
Triangle, Incenter, Parallel to a side, Angle, Congruence.

Proposed Problem 377.
Triangle, Internal Angle Bisector, Altitude.

Proposed Problem 376.
Triangle, Excenter, Internal and External Angle Bisectors.

Proposed Problem 375.
Triangle, Excenter, External Angle Bisectors.

Proposed Problem 374.
Triangle, Incenter, Internal Angle Bisectors.

Proposed Problem 373.
Square, Inscribed Circle, Diagonal, Perpendicular, Angle.

Proposed Problem 372.
Circles, Common Internal and External Tangent, Angles.

Proposed Problem 371.
Square, Inscribed circle, Triangle, Area.

Proposed Problem 370.
Triangle with squares, Circumcircles, Tangent circles.

Proposed Problem 369.
Intersecting circles, Chord, Center, Angle, Congruence.

Proposed Problem 366.
Scalene triangle, Circumcircle, Angles, 60 Degrees, Equilateral triangle.

Proposed Problem 365.
Circular Sector of 60 degrees, Midpoints, Perpendicular, Congruence.

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

Proposed Problem 362.
Circle, Chord, Perpendicular, Equal chords.

Proposed Problem 361.
Right triangle, Incircle, Incenter, Tangency points, Angle.

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

Proposed Problem 359.
Cyclic quadrilateral, Angle bisector, Rhombus.

Proposed Problem 358.
Isosceles triangle 80-80-20, Circle, Angles, Congruence.

Proposed Problem 355.
Circles, Common external tangent, Concyclic points.

Proposed Problem 352.
Tangential quadrilateral, Incircles, Common tangent, Circumscribable or Tangential quadrilateral.

Proposed Problem 351.
Rhombus, Incircles, Common tangent, Circumscribable or Tangential quadrilateral.

Proposed Problem 350.
Triangle, Cevian, Incircles, Tangents, Tangency Point, Angles.

Proposed Problem 349.
Triangle, Cevian, Incircles, Tangents, Tangency Point.

Proposed Problem 348.
Circles, Common External Tangents, Common Internal Tangent.

Proposed Problem 347.
Triangle, Altitude, Perpendicular, Circle, Concyclic points.

Proposed Problem 346.
Equal circles, Tangents, Hexagon, Semiperimeter.

Proposed Problem 345.
Equal circles, Tangents, Concurrent lines, Hexagon, Semiperimeter.

Proposed Problem 344.
Quadrilateral, Extension of sides, Circle, Tangent, Semiperimeter.

Proposed Problem 343.
Hexagon, Inscribed circle, Tangent, Semiperimeter.

Proposed Problem 342.
Pentagon, Inscribed circle, Tangent, Semiperimeter.

Proposed Problem 341.
Triangle, Inscribed circle, Tangent, Semiperimeter.

Proposed Problem 338.
Triangle, Circumcircle, Inscribed Circle, Exterior angle bisector, Concyclic points.

Proposed Problem 337.
Isosceles Trapezoid, Angle bisector, Parallel, Concyclic points.

Proposed Problem 336.
Two equal circles, a Common Tangent and a Square.

Proposed Problem 335.
Cyclic Quadrilateral, Perpendiculars to Sides.

Proposed Problem 334.
Cyclic Quadrilateral, Perpendiculars to Diagonals.

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

Proposed Problem 332.
Cyclic quadrilateral, Ratio of diagonals, Similarity.

Proposed Problem 331.
Square, Point on the Inscribed Circle, Tangency Points.

Proposed Problem 330.
Cyclic quadrilateral, Perpendicular diagonals, Area, Circumcenter.

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

Proposed Problem 328.
Triangle, Incircle, Tangency Points, Parallel, Midpoint.

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

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

Proposed Problem 325.
Isosceles triangle, Altitude, Cevian, Incircle, Excircle.

Proposed Problem 323.
Triangle, Incenter, Circumcenter, Equal circles, Collinearity.

Proposed Problem 322.
Square, Inscribed circle, Tangent, Triangle area.

Proposed Problem 320.
Triangle, Circumcircle, Incenter, Excenter, Collinear points.

Proposed Problem 316.
Circular segments and Inscribed Squares.

Proposed Problem 315.
Three Tangent circles, Common external tangent line, Geometric Mean.

Proposed Problem 314.
Tangent circles, Common external tangent line, Geometric Mean.

Proposed Problem 313.
Circle, Chord, Tangent, Perpendicular, Geometric Mean.

Proposed Problem 312.
Cyclic quadrilateral, Side extensions, Tangents.

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

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

Proposed Problem 309.
Regular Nonagon or Enneagon, Diagonals, Side.

Proposed Problem 308.
Regular Nonagon or Enneagon, Midpoints, Side, Arc, Angle.

Proposed Problem 307.
Regular Nonagon or Enneagon, Midpoints, Side, Arc, Angle.

Proposed Problem 301.
Tangents to a circle, Secants, Square.

Proposed Problem 300.
Tangent to a circle, Secants, Square.

Proposed Problem 299.
Intersecting Circles, Chord, Secant, Midpoint, Congruence.

Proposed Problem 298.
Intersecting Circles, Chord, Secant, Midpoint, Congruence.

Proposed Problem 297.
Intersecting Circles, Chord, Secant, Radius, Angle, Perpendicular.

Proposed Problem 296.
Intersecting Circles, Chord, Radius, Angle, Perpendicular.

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

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

Proposed Problem 293.
Inscribed Quadrilateral, Perpendicular, Rectangle, Isosceles Right triangle, Area, Similarity.

Proposed Problem 291.
Triangle, Circle, Circumradius, Perpendicular.

Proposed Problem 290.
Internally Tangent circles, Radius, Perpendicular, Tangent.

Geometry Expressions.

Proposed Problem 289: Tangent circles, Radius, Perpendicular, Tangent.

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

Congruence. Index.

Similarity, Ratios, Proportions. Index.

Areas Index

Sagitta, Arc, Chord.

Pi Day.
Saturday, March 14, 2009 = 3.14
It's time to get irrational. Tomorrow is Pi Day, when mathematicians will gather to celebrate the mystery of science's most famous strange number.

Go Geometry Education Index

Proposed Problem 291.
Triangle, Circle, Circumradius, Perpendicular.

Proposed Problem 290.
Internally Tangent circles, Radius, Perpendicular, Tangent.

Proposed Problem 289.
Tangent circles, Radius, Perpendicular, Tangent

Proposed Problem 285.
Circular Sector 90 degrees, Semicircles, Circle, Tangent, Radius.

Proposed Problem 284.
Circular Sector 90 degrees, Semicircles, Tangent, Radius.

Proposed Problem 283.
Circular Sector 90 degrees, Semicircle, Circle inscribed, Radius.

Proposed Problem 279.
Tangent Circles, Common External Tangent, Chords, Inradius.

Proposed Problem 278.
Tangent Circles, Common External Tangent, Chord.

Proposed Problem 277.
Tangent Circles, Common External Tangent.

Proposed Problem 276.
Square, 90 degree Arcs, Circle, Radius.

Proposed Problem 275.
Right Triangle, Circumcircle, Sagitta, Inradius.

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

Proposed Problem 270.
Tangent Circles, Common external tangent, Fractional exponents.

Proposed Problem 262.
Regular Hexagon inscribed in a circle, sum of distances.

Proposed Problem 261.
Regular Pentagon inscribed in a circle, sum of distances.

Proposed Problem 257.
Equilateral Triangle, Circumcircle, Point, Vertices, Side, Distances, Squares.

Proposed Problem 256.
Equilateral Triangle, Circumcircle, Point, Vertices, Distances.

Proposed Problem 248.
Napoleon's Theorem III. Inner and outer Napoleon triangles, Area.

Proposed Problem 247.
Napoleon's Theorem II. Internal Equilateral triangles. Inner Napoleon triangle.

Proposed Problem 246.
Napoleon's Theorem I. External Equilateral triangles. Outer Napoleon triangle.

Proposed Problem 220. Right Triangle, Altitude, Angle Bisector, Distance, Arithmetic Mean.  

Proposed Problem 215. Quadrilateral, Angle Bisectors, and Cyclic Quadrilateral.

Proposed Problem 213. Triangle, Incircle, Inradius, Semicircles, Common Tangents.  

Archimedes Arbelos and Square 2. Dynamic Geometry Software.
Step-by-Step construction, Manipulation, and animation. 

Archimedes Arbelos and Square 1. Dynamic Geometry Software.
Step-by-Step construction, Manipulation, and animation. 

Proposed Problem 209. Triangle, Incircles, Inradius.  

Proposed Problem 195. Area of a Triangle, Inradius, Exradii.  

Proposed Problem 208. Triangle, Excircles, Angles, 360 degrees.  

Proposed Problem 207. Right Triangle, Hypotenuse, Inradius, Exradius relative to the hypotenuse.  

Proposed Problem 206. Area of a Right Triangle, Inradius, andExradius relative to the hypotenuse.  

Proposed Problem 205. Right Triangle Area, Exradii relatives to legs or catheti.  

Proposed Problem 204. Right Triangle, Incircle, Excircles, Inradius, Exradii.  

Proposed Problem 203. Right Triangle, Excircles, Exradii, Hypotenuse.  

Proposed Problem 202. Right Triangle, Incicrle, Excircles relatives to catheti, Points of Tangency, Exradius, Semiperimeter.

Proposed Problem 201. Right Triangle, Excircles, Points of Tangency, Exradius, Semiperimeter.

Proposed Problem 200. RightTriangle, Incircle, Excircles, Points of Tangency, Inradius.

Proposed Problem 197. Area of a Triangle, Side, Inradius, and Exradius.

Proposed Problem 196. Triangle, Inradius and Exradii Formula.

Proposed Problem 195. Area of a Triangle, Inradius, Exradii.

Proposed Problem 194. Area of a Triangle, Semiperimeter, Exradius.

Proposed Problem 193. Area of a Triangle, Semiperimeter, Inradius.

Proposed Problem 192. Circle, Diameter, Chord, Perpendicular, Triangle, Area.

Proposed Problem 190. Tangent circles, Tangent chord, Perpendicular, Distance.

Proposed Problem 187. Right Triangle, Altitude, Incenters, Circles, Angles.

Proposed Problem 186. Right Triangle, Altitude, Incenters, Circles.

Proposed Problem 182. Overlapping Circles, Find an angle.

Proposed Problem 181. Circular Sector of 90 degrees, find an angle.

Proposed Problem 180. Circles Tangent Externally, Common External Tangents, Areas.

Go to Page: Previous | 1 | 2 | 3 | 4 | 5 | Next