Two circles, a rectangle and two line segments. Prove that the red points are collinear.
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The small cog
Category: Intermediate
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A walk in the park
Two squares sharing a vertex and a line segment. What’s the yellow area?
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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?
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The personal letter
Two rectangles share two vertices. What’s the green fraction?
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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?
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The skew bridge
Two points are on opposite sides of a channel. A skew bridge, which has a fixed direction (for instance North East), can be placed anywhere along the channel. Where to place it such that the path from A to B over the bridge is the shortest?
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To the max
Two squares and two line segments. If the angle α is maximal, what is yellow : red?