A regular pentagon and a right triangle. What’s the angle α?
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It’s all right II
Tag: triangle
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Bond of union
Two intersecting circles with two inscribed triangles and two line segments through an intersection point. Prove that the triangles are similar.
Co-author: Marshall W. Buck.
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Centre of attraction
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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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?
Author: Marshall W. Buck.
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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.
Proposed by Marshall W. Buck. Note that this problem is known as the Blanchet Theorem.