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Quadrilaterals: Table of
Content (Page 4 of 4)
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Square
Proposed
Problem 76: Area of a Circle.
Square, Circle, Circular Sector. |
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Proposed Problem 74: Three Intersecting Circles.
Cyclic quadrilateral, Angles.
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Proposed Problem 73: Three Intersecting Circles.
Cyclic quadrilateral.
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Proposed Problem 72: Intersecting Circles.
Cyclic quadrilateral, Chords, Parallel.
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Proposed Problem 71: Cyclic Quadrilateral.
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Proposed Problem 70: Squares inscribed in a triangle, Similarity.
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Proposed Problem 69: Square inscribed in a triangle, Similarity.
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Proposed Problem 67: Triangle, Circumcircle, Angles, Cyclic
Quadrilateral.
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Four Circles Theorem Using TracenPoche Dynamic Software
Step-by-Step construction, Manipulation, and animation. |
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Proposed Problem 63: Heptagon
Regular, Side and Diagonals.
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Proposed Problem 62: Square
Diagonal, Inscribed Circle.
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Arbelos, Inscribed Circle and Concyclic Points
Cyclic Quadrilateral. |
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Casey's Theorem. Generalized Ptolemy's Theorem. |
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Proposed Problem 57: Angle bisector, circles
Cyclic Quadrilateral. |
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Proposed Problem 55: Angle bisector, circles
Cyclic Quadrilateral. |
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Generalizing Van Aubel: Michael de Villiers' Theorems.
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Eyeball Theorem:
Animated Angle to Geometry Study.
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Eyeball to Eyeball Theorem
Presentation: "Animated
Angle to Geometry Study I & II." 46th Annual Georgia Mathematics
Conference, Extreme Makeover: Mathematics Edition!, Rock Eagle,
October 20-22, 2005, |
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Hippocrates and Squaring the Circle
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Triangle with Squares
Problem
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Thébault's Theorem. Parallelogram with Squares theorem
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Varignon and Wittenbauer parallelograms. Quadrilateral: midpoints and
trisection points of the edges.
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Van Aubel's Theorem.
Quadrilateral with Squares. Proof with animation.
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Equilic Quadrilateral.
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Ptolemy's Theorem.
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Cyclic
Quadrilateral: Ratio of the Diagonals
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Brahmagupta's Theorem
Cyclic quadrilateral.
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Brahmagupta's Corollary
Cyclic quadrilateral.
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Brahmagupta's Formula
Area of a cyclic quadrilateral.
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Brahmagupta Formula
Extension
Area of any quadrilateral.
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Newton's
Theorem: Newton's Line. Circumscribed quadrilateral, midpoints of
diagonals, center of the circle inscribed.
Puzzle of the Newton's
Theorem: 50 pieces of circles. |
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Sangaku Problem. The
incenters of four triangles in a cyclic quadrilateral form a rectangle. |
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Complete Quadrilateral Theorems
Presentation: "Animated
Angle to Geometry Study I & II." 46th Annual Georgia Mathematics
Conference, Extreme Makeover: Mathematics Edition!, Rock Eagle,
October 20-22, 2005, |
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Kurschak's Tile and Theorem.
Jozsef Kurschak (Hungary, 1864-1933) An elegant and a purely geometric
way of finding the area of a regular dodecagon.
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Proposed Problem 33.
Triangle and quadrilateral. |
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Proposed
Problem 35.
Incenters and Inradii in Cyclic Quadrilateral. |
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Proposed Problem 42.
Angles and triangles. |
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