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
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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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A tight squeeze
Two intersecting circles inside a rectangle and a line segment connecting vertex, intersection point and tangency point. What’s the angle α?
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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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Tumbler doll II
Three squares and a circle. The red point is a common intersection of two square sides and the circle. What is blue : green?
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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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Circle dancing
Start with a blue triangle, and form the green triangle whose vertices bisect each circular arc connecting blue vertices. Similarly, make the red triangle from the green, and the orange triangle from the red. Prove the triangle becomes equilateral in the limit.