A unit square paper is folded as shown. What is the red area?
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Folded napkin II
Author: Rik D. Tangerman
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Tip the scale
Two equilateral triangles and a square. What’s the angle α?
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The cheese dome
A semicircle and two tangent circles (tangency point shown). What is the angle α?
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Half right
A right triangle with two angle bisectors. What is red : blue?
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Your turn
A regular hexagon of which the centre is a vertex of an equilateral triangle. What is the angle α?
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The high-water mark
Two equilateral triangles on a blue line segment. Prove that the red line segment is parallel to it.
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The crown II
Several triangles and three congruent angles. Prove that the red point is the incentre of the yellow triangle.
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The camping
A square containing an isosceles triangle. What’s the angle α?
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Hidden perfection
Two squares and two equilateral triangles. Prove that the red vertices also form an equilateral triangle.
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The green diamond
Two equilateral triangles are placed side by side. The common (blue) side is extended. What is red : blue?