A triangle with an inscribed triangle. What fraction of the former does the latter cover in terms of lengths a, b, c, d, e and f?
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Spiegel im Spiegel
Author: Rik D. Tangerman
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The lever of Archimedes
Two congruent triangles are placed as shown. A line segment passes through the centroid of the yellow triangle. What’s the proportion a : b?
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The green necktie
A square with several line segments. What fraction is green?
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House of Orange
A right triangle with a red and yellow square attached. Two circular arcs centered in the triangle vertices. What is the area of the orange rectangle in terms of red and yellow?
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Out of proportion
An equilateral triangle containing a parallelogram, another equilateral triangle and a circular arc that is tangent in its base vertices. What is the proportion pink : blue?
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Head above water
A unit square with an extended side immersed in another square. What is the area of the red triangle?
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The framing effect
Four squares, three of which are coloured. What’s the area of the blue one?
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A dangerous step
Three squares are placed in a row. Prove that the red vertices are collinear.
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Projection bias
Two regular pentagons are placed side by side. What’s the proportion blue : green?
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Circular architecture
An equilateral triangle and two circles. The centre of the right circle is the triangle side midpoint. Both circle intersections lie on a triangle side. Prove that the three red circular arcs are congruent.