A triangle, its incircle and a right triangle. The circle centre is shown in blue. Prove that the tangency points and right triangle vertex are collinear.
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The right position
Tag: triangle
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The Pythagoras bug
Two blue squares and two red right triangles. What are the proportions of the triangle sides?
Author: Matthew Arcus.
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The Suresh triplet
Two squares share a vertex. What’s blue : green : orange?
An equilateral triangle and three line segments. What’s the angle α?
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The prisoners dilemma
Two prisoners are chained to the walls of a triangular cell. The base is covered with a mirror and a perpendicular wall is separating them. They can each see the opposite corner through a hole. Proof they can see each other through another hole at the base of the perpendicular.
Note that this problem is known as the Blanchet Theorem.
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The reflection principle
A green triangle with several line segments. Prove that the red point is its orthocentre.
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The dug-in heel
A rectangle containing a right triangle. What’s red : blue?
From the purple triangle ABC and the center of its inscribed circle at D, form the three colored circles (BDC), (CDA), and (ADB), with centers F, G, H, respectively, thus forming the yellow triangle FGH. Prove that there is one circle that circumscribes both triangles.
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Egg basket II
What fraction of the regular hexagon is yellow?
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The meeting point
Two squares and an equilateral triangle. The three red line segments meet in a point. What is the yellow fraction?