An equilateral triangle with two perpendiculars to a point that is at the same height as the triangle centre. What is red : yellow?
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Centre of attraction
Tag: triangle
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The chessboard hallucination
Behold a 13-14-15 triangle. The 15-long side is dissected into 5 equal parts and the 14-long side is dissected into 7 equal parts. What is the difference between the red and green areas?
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The personal letter
Two rectangles share two vertices. What’s the green fraction?
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The right position
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 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?