Three triangles are glued together. The green ones are based on a common line. What’s the angle α?
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Two brotherly pines
Category: Intermediate
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A light packing
A triangle containing two congruent squares. Each square has 1/3 the perimeter and 1/6 the area of the triangle. What’s the triangle side length proportion a : b : c?
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Uneven cups
Two semicircles and several line segments. Prove that the red line segments are parallel.
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The glass splinter
A triangle of which two sides and one angle are given. What’s the angle α?
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The seesaw
A regular hexagon with three diagonals and two line segments at right angles. What is the proportion green : yellow : blue : orange?
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The Zamani suggestion
Two regular hexagons share a vertex. What’s the area proportion red : yellow hexagon?
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The purple square
A regular octagon of side length 2 with two diagonals and a square. What is the purple area?
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Pushing the boundary
Two equilateral triangles are placed side by side. What’s the proportion green : red?
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The Pyramid of Austerlitz
An equilateral triangle and a parabola that is tangent to two of its sides in two vertices. Proof that the triangle centre coincides with the parabola focus.
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A deep connection
Two squares inside a circle. What is the circle area in terms of length a?