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

Circumcenter. Index.

Incenter of a triangle. Index.

Excenter. Index.
Excircle, Exradius.

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

Intersecting Circles Index.
Theorems and Problems.

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.

Equilic Quadrilateral.
 

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.

Geometry Expressions.

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.

Proposed Problem 160. Triangle, Incircle, Incenter, Circumcircle, Circumcenter, Inradius.

Proposed Problem 159. Distances from the Circumcenter to the Incenter and the Excenters.

Proposed Problem 158. Relation between the Circumradius, Inradius and Exradii of a triangle.

Proposed Problem 157. Distance from the Circumcenter to the Excenter.

Proposed Problem 156. Triangle, Circumradius, Exradius, Chord, Secant line.  

Proposed Problem 155. Euler's Theorem: Distance from the Incenter to the Circumcenter.  

Proposed Problem 154. Triangle, Inradius, Circumradius, Chord.  

Proposed Problem 153. Circumscribed Quadrilateral, Diagonals Concurrent with Chords.  

Proposed Problem 152. Circumscribed Quadrilateral, Diagonal, Chord, Proportion.  

Machu Picchu and Golden Rectangle.  

Chichen Itza and Golden Rectangle.  

Christ the Redeemer and Golden Rectangle.  

Colosseum and Golden Rectangle.  

Petra and Golden Rectangle.  

Proposed Problem 145. Four Triangles, Incircle, Tangent and Parallel to Side, Incenters, Circumcenters.  

Proposed Problem 144. Four Triangles, Incircle, Tangent and Parallel to Side, Inradii.  

Proposed Problem 143. Four Triangles, Incircle, Tangent and Parallel to Side, Circumradii.  

Proposed Problem 142. Four Triangles, Incircle, Tangent and Parallel to Side, Areas.  

Proposed Problem 141. Triangle, Incircle, Tangent , Parallel, Perimeters.  

Proposed Problem 140. Triangle, Excircle, Tangent, Semiperimeter.  

Proposed Problem 136. Orthic Triangle, Altitudes, Perpendicular, Concyclic Points.  

Interactive Gergonne Line and Nobbs Points. Dynamic Geometry.
Step-by-Step construction, Manipulation, and animation.

Interactive Simson Line. Dynamic Geometry.
Step-by-Step construction, Manipulation, and animation.

Triangle, Three Medians, Six Concyclic Circumcenters. Dynamic Geometry.
Step-by-Step construction, Manipulation, and animation.
Prove proposition.

Triangle: Incircle, Perpendicular, Angle Bisector. Dynamic Geometry.
Step-by-Step construction, Manipulation, and animation.
Prove proposition.

Proposed Problem 128. Incenter of a Triangle, Angle Bisectors, Sum of Ratios.

Geometry in Action. Reuleaux's rotor: How Round is your Circle?

Proposed Problem 127. Centroid and Incenter of a Triangle, Parallel, Proportions.

Proposed Problem 126. Incenter of Triangle, Angle Bisector, Proportions.

Proposed Problem 120. Area of triangle, incenter, excircles, tangent.

Proposed Problem 119. Area of triangle, incenter, excircle, tangent.

Proposed Problem 118. Area of triangle, incenter, excenter, tangent.

Proposed Problem 117. Area of triangle, incenter, excircles, tangent.

Proposed Problem 116. Area of triangle, excircles, tangent.

Proposed Problem 115. Area of triangle, excircles, tangent.

Proposed Problem 114. Area of triangle, incircle, excircle.

Proposed Problem 113. Area of triangle, incircle, excircle.

Stonehenge builders had geometry skills to rival Pythagoras
Five years of detailed research, carried out by the Oxford University landscape archaeologist Anthony Johnson, claims that Stonehenge was designed and built using advanced geometry.

Proposed Problem 112. Area of square and triangle.

Proposed Problem 111. Orthogonal Circles.

Proposed Problem 110. Area of Contact Triangle.

Bandurria is the oldest Peruvian archaeological site, says expert
Bandurria may rival Caral as oldest citadel in Americas.
Satellite View: circular ceremonial center

Eight-Point Circle Theorem
Step-by-Step construction, Manipulation, and animation.

Proposed Problem 100. Circle Area, Archimedes' Book of Lemmas.

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

Incircles or inscribed circles.
Proposed Problem 96. Similar Triangles, Incenters, Parallelogram.

Incircles or inscribed circles.
Proposed Problem 95. Similar Triangles, Inradii, Parallel.

Circumcircles or circumscribed circle
Proposed Problem 94. Similar Triangles, Circumcircles, Circumradii.

Circumcircles or circumscribed circle
Proposed Problem 93. Similar Triangles, Circumcircles, Parallelogram.

Circumcircles or circumscribed circle
Proposed Problem 92. Similar Triangles, Circumcircles, Circumradii, Parallel.

Intouch and Extouch Triangles. Puzzle cut: 20 Piece Classic
Based on Proposed Problem 86.

Proposed Problem 86. Intouch and Extouch Triangles, Areas.

Taylor Circle Theorem Using TracenPoche Dynamic Software
Step-by-Step construction, Manipulation, and animation.
Henry Martyn Taylor and the blind student of mathematics

Proposed Problem 85. Contact Triangles Areas, Incircle, Excircle.

Proposed Problem 84. Contact Triangles Areas, Incircle, Excircle, Inradius, Exradius.

Proposed Problem 83. Area of the Excircle Contact Triangle, exradius, circumradius.

Proposed Problem 82. Area of the Contact Triangle, inradius, circumradius.

Proposed Problem 81. Area of a triangle, side, inradius, circumradius.

Proposed Problem 80. Area of a triangle, side, incircle, inradius.

Proposed Problem 79: Triangle. Similarity, Altitudes, Orthocenter, Incircles, Inradii.

Proposed Problem 78: Angles of a Circle. Perpendicular and parallel lines, Midpoint, Diameter, Chord, Cyclic quadrilateral, Congruence.

Proposed Problem 77: Angles of a Circle. Parallel lines, Cyclic quadrilateral.

I have used Geometry Expressions, the world's first Interactive Symbolic Geometry System, to visualize the Archimedean Twins and check out a variety of conjectures.

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