A semicircle containing two circles and two triangles. The blue right triangle connects three tangency points. Prove it is isosceles.
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Sisyphus
Month: June 2021
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The triangle trio
Three triangles, one of which is right and one is isosceles, form a large triangle. Two side lengths are given. What fraction of the total area is red?
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The ragged mountain
A square containing three line segments of given length. What fraction is green?
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The two jabs
Two congruent equilateral triangles share a vertex. What is the angle α?
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The single parent holiday
An equilateral triangle containing two circles of given area and a common tangent divided in two. What is the proportion of the two parts?
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The birdwatcher
Two congruent circles and a right triangle inside a semicircle. What fraction is blue?
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The tin foil hat
A circle inside a quarter circle. The triangle connects the two tangency points and the top of the quarter circle. What’s the angle α?
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The hammock
A square inscribed in a triangle. Two areas are given. What is the square’s area?
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Lazy Friday
Four congruent squares plus another one. What is the angle α?
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The fez
A circle and a semicircle inside a square. What’s the length proportion of the two chords?