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Circles, Theorems and Problems: Table of Content
(Page 1 of 5)
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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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Intersecting Circles Index.
Theorems and Problems. |
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Proposed Problem
301.
Tangents to a circle, Secants, Square. |
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Proposed Problem
300.
Tangent to a circle, Secants, Square. |
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Proposed Problem 299.
Intersecting Circles, Chord, Secant, Midpoint, Congruence. |
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Proposed Problem 298.
Intersecting Circles, Chord, Secant, Midpoint, Congruence. |
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Proposed Problem 297.
Intersecting Circles, Chord, Secant, Radius, Angle, Perpendicular. |
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Proposed Problem 296.
Intersecting Circles, Chord, Radius, Angle, Perpendicular. |
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Proposed Problem 295.
Archimedean Twin Circles, Arbelos, Semicircles, Harmonic Mean, Radii, Perpendicular. |
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Proposed Problem 294.
Right triangle, Circumcenter, Excenter, Hypotenuse, Perpendicular. |
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Proposed Problem 293.
Inscribed Quadrilateral, Perpendicular, Rectangle, Isosceles Right triangle, Area, Similarity. |
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Proposed Problem 291.
Triangle, Circle, Circumradius, Perpendicular. |
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Proposed Problem 290.
Internally Tangent circles, Radius, Perpendicular, Tangent. |
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Geometry Expressions. |
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Proposed Problem 289:
Tangent circles, Radius, Perpendicular, Tangent. |
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Proposed Problem 288:
Tangent circles, Harmonic Mean, Radius, Diameter. |
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Congruence.
Index.
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Similarity, Ratios, Proportions.
Index.
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Areas Index |
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Sagitta, Arc, Chord. |
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Equilic Quadrilateral.
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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. |
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Go Geometry
Education Index |
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Proposed Problem 291.
Triangle, Circle, Circumradius, Perpendicular. |
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Proposed Problem 290.
Internally Tangent circles, Radius, Perpendicular, Tangent. |
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Geometry Expressions. |
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Proposed Problem 289.
Tangent circles, Radius, Perpendicular, Tangent |
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Proposed Problem 285.
Circular Sector 90 degrees, Semicircles, Circle, Tangent, Radius. |
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Proposed Problem 284.
Circular Sector 90 degrees, Semicircles, Tangent, Radius. |
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Proposed Problem
283.
Circular Sector 90 degrees, Semicircle, Circle inscribed, Radius. |
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Proposed Problem
279.
Tangent Circles, Common External Tangent, Chords, Inradius. |
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Proposed Problem
278.
Tangent Circles, Common External Tangent, Chord. |
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Proposed Problem
277.
Tangent Circles, Common External Tangent. |
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Proposed Problem
276.
Square, 90 degree Arcs, Circle, Radius. |
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Proposed Problem
275.
Right Triangle, Circumcircle, Sagitta, Inradius. |
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Proposed Problem
271.
Tangent Circles, the Cube of the Common external tangent. |
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Proposed Problem
270.
Tangent Circles, Common external tangent, Fractional exponents. |
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Proposed Problem
262.
Regular Hexagon inscribed in a circle, sum of distances. |
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Proposed Problem
261.
Regular Pentagon inscribed in a circle, sum of distances.
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Proposed Problem
257.
Equilateral Triangle, Circumcircle, Point, Vertices, Side, Distances,
Squares.
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Proposed Problem
256.
Equilateral Triangle, Circumcircle, Point, Vertices, Distances.
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Proposed Problem
248.
Napoleon's Theorem III. Inner and outer Napoleon triangles, Area.
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Proposed Problem
247.
Napoleon's Theorem II. Internal Equilateral triangles. Inner Napoleon
triangle.
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Proposed Problem
246.
Napoleon's Theorem I. External Equilateral triangles. Outer Napoleon
triangle.
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Proposed Problem
220. Right Triangle, Altitude, Angle Bisector, Distance, Arithmetic Mean.
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Proposed Problem
215.
Quadrilateral, Angle Bisectors, and Cyclic
Quadrilateral.
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Proposed Problem
213. Triangle, Incircle, Inradius, Semicircles, Common Tangents. |
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Archimedes Arbelos and Square
2.
Dynamic Geometry Software.
Step-by-Step construction, Manipulation, and animation. |
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Archimedes Arbelos and Square 1.
Dynamic Geometry Software.
Step-by-Step construction, Manipulation, and animation. |
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Proposed Problem
209. Triangle, Incircles, Inradius. |
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Proposed Problem
195. Area of a Triangle, Inradius, Exradii. |
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Proposed Problem
208. Triangle, Excircles, Angles, 360 degrees. |
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Proposed Problem
207. Right Triangle, Hypotenuse, Inradius, Exradius relative to the hypotenuse. |
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Proposed Problem
206. Area of a Right Triangle, Inradius, andExradius relative to the hypotenuse. |
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Proposed Problem
205. Right Triangle Area, Exradii relatives to legs or catheti. |
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Proposed Problem
204. Right Triangle, Incircle, Excircles, Inradius, Exradii. |
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Proposed Problem
203. Right Triangle, Excircles, Exradii, Hypotenuse. |
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Proposed Problem
202. Right Triangle, Incicrle, Excircles relatives to catheti, Points of Tangency, Exradius, Semiperimeter. |
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Proposed Problem
201. Right Triangle, Excircles, Points of Tangency, Exradius, Semiperimeter. |
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Proposed Problem
200. RightTriangle, Incircle, Excircles, Points of Tangency, Inradius. |
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Proposed Problem
197. Area of a Triangle, Side, Inradius, and Exradius. |
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Proposed Problem
196. Triangle, Inradius and Exradii Formula. |
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Proposed Problem
195. Area of a Triangle, Inradius, Exradii. |
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Proposed Problem
194. Area of a Triangle, Semiperimeter, Exradius. |
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Proposed Problem
193. Area of a Triangle, Semiperimeter, Inradius. |
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Proposed Problem
192. Circle, Diameter, Chord, Perpendicular, Triangle, Area. |
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Proposed Problem
190. Tangent circles, Tangent chord, Perpendicular, Distance. |
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Proposed Problem
187. Right Triangle, Altitude, Incenters, Circles,
Angles. |
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Proposed Problem
186. Right Triangle, Altitude, Incenters, Circles. |
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Proposed Problem
182. Overlapping Circles, Find an angle. |
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Proposed Problem
181. Circular Sector of 90 degrees, find an angle. |
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Proposed Problem
180. Circles Tangent Externally, Common External Tangents, Areas. |
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Proposed Problem
160. Triangle, Incircle, Incenter, Circumcircle, Circumcenter, Inradius. |
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Proposed Problem
159. Distances from the Circumcenter to the Incenter and the Excenters. |
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Proposed Problem
158. Relation between the Circumradius, Inradius and Exradii of a triangle. |
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Proposed Problem
157. Distance from the Circumcenter to the Excenter. |
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Proposed Problem
156. Triangle, Circumradius, Exradius, Chord, Secant line. |
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Proposed Problem
155. Euler's Theorem: Distance from the Incenter to the Circumcenter. |
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Proposed Problem
154. Triangle, Inradius, Circumradius, Chord. |
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Proposed Problem
153. Circumscribed Quadrilateral, Diagonals Concurrent with Chords.
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Proposed Problem 152. Circumscribed Quadrilateral, Diagonal, Chord, Proportion.
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Machu Picchu and Golden Rectangle.
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Chichen Itza and Golden Rectangle.
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Christ the Redeemer and Golden Rectangle.
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Colosseum and Golden Rectangle.
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Petra and Golden Rectangle.
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Proposed Problem
145.
Four Triangles, Incircle, Tangent and Parallel to Side, Incenters, Circumcenters. |
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Proposed Problem
144. Four Triangles, Incircle, Tangent and Parallel to Side, Inradii. |
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Proposed Problem
143. Four Triangles, Incircle, Tangent and Parallel to Side, Circumradii. |
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Proposed Problem
142. Four Triangles, Incircle, Tangent and Parallel to Side, Areas. |
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Proposed Problem
141. Triangle, Incircle, Tangent
, Parallel, Perimeters. |
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Proposed Problem
140. Triangle, Excircle, Tangent, Semiperimeter. |
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Proposed Problem
136. Orthic Triangle, Altitudes, Perpendicular, Concyclic Points. |
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Interactive
Gergonne Line and Nobbs Points.
Dynamic Geometry.
Step-by-Step construction, Manipulation, and animation. |
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Interactive
Simson Line.
Dynamic Geometry.
Step-by-Step construction, Manipulation, and animation. |
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Triangle,
Three Medians, Six Concyclic Circumcenters.
Dynamic Geometry.
Step-by-Step construction, Manipulation, and animation.
Prove proposition. |
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Triangle: Incircle, Perpendicular, Angle Bisector.
Dynamic Geometry.
Step-by-Step construction, Manipulation, and animation.
Prove proposition. |
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Proposed Problem
128. Incenter of a Triangle, Angle Bisectors, Sum of Ratios.
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Geometry
in Action. Reuleaux's rotor: How Round is your Circle?
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Proposed Problem
127. Centroid and Incenter of a Triangle,
Parallel, Proportions.
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Proposed Problem
126. Incenter of Triangle, Angle Bisector, Proportions.
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Proposed Problem
120. Area of triangle,
incenter, excircles,
tangent.
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Proposed Problem
119. Area of triangle,
incenter, excircle,
tangent.
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Proposed Problem
118. Area of triangle,
incenter, excenter,
tangent.
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Proposed Problem
117. Area of triangle,
incenter, excircles,
tangent.
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Proposed Problem
116. Area of triangle, excircles,
tangent.
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Proposed Problem
115. Area of triangle, excircles,
tangent.
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Proposed Problem
114. Area of triangle, incircle,
excircle.
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Proposed Problem
113. Area of triangle, incircle,
excircle.
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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.
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Proposed Problem
112. Area of square and triangle.
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Proposed Problem
111. Orthogonal Circles.
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Proposed Problem
110. Area of Contact Triangle.
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Bandurria is the oldest Peruvian archaeological site, says expert
Bandurria may rival Caral as oldest citadel in Americas.
Satellite View: circular ceremonial center |
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Eight-Point Circle Theorem
Step-by-Step construction, Manipulation, and animation. |
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Proposed Problem
100. Circle Area, Archimedes' Book of Lemmas.
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Proposed Problem 99: Circle Area, General Extension to Pythagoras' Theorem.
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Incircles or inscribed circles.
Proposed Problem
96. Similar Triangles, Incenters, Parallelogram. |
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Incircles or inscribed circles.
Proposed Problem
95. Similar Triangles, Inradii,
Parallel. |
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Circumcircles or circumscribed circle
Proposed Problem
94. Similar Triangles, Circumcircles,
Circumradii. |
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Circumcircles or circumscribed circle
Proposed Problem
93. Similar Triangles, Circumcircles, Parallelogram. |
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Circumcircles or circumscribed circle
Proposed Problem
92. Similar Triangles, Circumcircles, Circumradii, Parallel. |
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Intouch and Extouch Triangles.
Puzzle cut: 20 Piece Classic
Based on Proposed Problem 86. |
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Proposed Problem
86. Intouch and Extouch Triangles, Areas. |
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Taylor Circle Theorem Using TracenPoche Dynamic Software
Step-by-Step construction, Manipulation, and animation.
Henry Martyn Taylor and the blind student of mathematics
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Proposed Problem
85. Contact Triangles Areas, Incircle, Excircle. |
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Proposed Problem
84. Contact Triangles Areas, Incircle, Excircle, Inradius, Exradius. |
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Proposed Problem
83. Area of the Excircle Contact
Triangle, exradius, circumradius. |
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Proposed Problem
82. Area of the Contact
Triangle,
inradius, circumradius. |
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Proposed Problem
81. Area of a triangle,
side, inradius, circumradius. |
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Proposed Problem
80. Area of a triangle,
side, incircle, inradius. |
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Proposed Problem
79: Triangle.
Similarity, Altitudes, Orthocenter, Incircles, Inradii. |
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Proposed Problem
78: Angles of a Circle.
Perpendicular and parallel
lines, Midpoint, Diameter, Chord, Cyclic quadrilateral, Congruence.
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Proposed Problem
77: Angles of a Circle. Parallel
lines, Cyclic quadrilateral.
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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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