An equilateral triangle and several line segments. What fraction is purple?
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The holy number
Author: Rik D. Tangerman
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Protection
Two coloured squares inside a triangle inside a square of side length a. What is the length proportion a : b?
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Elasticity
Four squares and two triangles. Prove that the two green angles are congruent.
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The miniature version
Two rectangles share a vertex. Two line segments connecting opposing vertices and the common side intersect in a single point. Prove that the rectangles are similar.
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Wheels in motion
Two tangent circles and a third circle touching the line segment connecting their centres in the tangency point. Prove that the red points (centre and two intersection points) are collinear.
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The Transamerica Pyramid
Two squares inscribed in a triangle. What fraction of its area is coloured?
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The three day stubble
A regular pentagon and a square share two vertices. What’s the angle α?
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It’s complicated
A circle, a semicircle and several triangles. The black points are tangency points. What proportions have the line segments a : r : b?
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The odd couple
A semicircle with two inscribed triangles The tangency points of the incircle of the bigger triangle are shown. What is the triangle area proportion orange : blue?
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Parallel universes
Two straight lines are specified by y=a+cx and y=b+cx, respectively, where b≥a. What’s the distance d between them in terms of a, b and c?