A regular nonagon and two equilateral triangles. What’s the angle α?
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Three times three
Author: Rik D. Tangerman
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The laser game
In an equilateral triangular mirror room a laser is shot from the top vertex down to the base. The light ray bounces three times to return to the same base point. What is the angle α?
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The hex division
A regular hexagon with two diagonals and two perpendiculars. What’s red : yellow?
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The owl of Ceva
A triangle with three concurring cevians. What’s orange : blue?
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In the red
Two congruent semicircles with their centres and a chord. Prove that the two red triangles are congruent as well.
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The vanilla ice cream
A regular pentagon with two extended sides and a right angle. What is blue : green?
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Wheel of fortune
A unit square and a point on the inscribed circle. What is a2+b2+c2+d2?
Three congruent squares share two vertices while the upper sides coincide. What’s red : blue?
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Falling pillar II
Three congruent rectangles on a line. Prove that the four red points are cyclic.
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The falling pillar
Three congruent rectangles on a line. What’s the angle α?