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Triangle with the
bisectors of the exterior angles. Collinearity. Key concept:
Menelaus Theorem.
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Ptolemy's Theorem.
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Cyclic
Quadrilateral: Ratio of the Diagonals
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Casey's Theorem. Generalized Ptolemy's Theorem.
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Pascal's Mystic Hexagram Theorem Proof |
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Eyeball Theorem:
Animated Angle to Geometry Study. |
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Butterfly Theorem
Proof with animation. |
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Monge &
d'Alembert Three Circles Theorem II with Dynamic Geometry. You can
alter the geometric construction dynamically in order to test and prove
(or disproved) conjectures and gain mathematical insight that is less
readily available with static drawings by hand. Requires Java
Plug-in 1.3 or higher. Please be patient while the applet loads on
your computer. |
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Monge &
d'Alembert Three Circles Theorem I with Dynamic Geometry. You can
alter the geometric construction dynamically in order to test and prove
(or disproved) conjectures and gain mathematical insight that is less
readily available with static drawings by hand. Requires Java
Plug-in 1.3 or higher. Please be patient while the applet loads on
your computer. |
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Blanchet Theorem
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Lemoine Theorem |
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Nagel Point
Theorem. Proof.
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Pentagons & Pentagrams. I found, exploring with dynamic geometry
software, new facts about pentagons and pentagrams. Key concept:
Menelaus Theorem.
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Interactive Hinged tessellation. Square tessellation - Dynamic Geometry.
Please be patient while the applet loads on your computer. This Java
applet requires Java 1.3 or higher. |
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Problem 99: Circle Area, General Extension
to Pythagoras' Theorem.
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Proposed Problem 62: Square
Diagonal, Inscribed Circle. |
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Proposed Problem 40.
Triangle, Incenter, Excenter, Angles 80, 40, Distances. |
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Proposed
Problem 40. Geometry Help.
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Sangaku
Proposed Problem 41. "Mickey Mouse."
Three circles, tangents, radii. |
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Proposed Problem 63: Heptagon
Regular, Side and Diagonals. |
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Morley's Triangle & Center: with interactive animation and
manipulation.
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Newton's
Theorem: Newton's Line. Circumscribed quadrilateral, midpoints of
diagonals, center of the circle inscribed.
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The Pythagorean Curiosity
Triangles and squares, fifteen conclusions. |
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Complete Quadrilateral: Ortholine-Steiner Line.
Step-by-Step construction, Manipulation, and animation |
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Newton's Theorem,
Newton-Gauss Line: Complete quadrilateral theorem. Using TracenPoche
Dynamic Geometry Software, Online
Step-by-Step construction, manipulation, and animation. |
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Archimedes'
Book of Lemmas. Exercise your brain. Archimedes wrote the "Book of
Lemmas" more than 2200 years ago. Solve these 15 high school level
problems and lift up your geometry skills.
Proposition 4, Arbelos, |
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Archimedes' Book of Lemmas.
Proposition 5,
Arbelos, Archimedean Twins.
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Archimedes' Book of Lemmas.
Proposition 6,
Arbelos,
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