Two touching circles and a common tangent. Three triangles are formed by tangency points and centres. What is the area of the green triangle X in terms of areas A and B?
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The commons
Category: Intermediate
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Softening the edges
A quarter circle contains a semicircle and a square. What fraction of the area is purple?
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The honeycomb
Two regular hexagons inscribed in a square. If the hexagons have side length a and b, what is the square’s side length?
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The folded napkin
A square sheet of paper is folded symmetrically from a corner. If the fold length is 4, what is the area of the triangle formed by the other three corners?
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Together we stand
Two squares sharing a vertex. What’s the angle α?
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The pleasure dome
A semicircle with three squares. The areas of the smaller squares are given. What is the area of the biggest one?
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Pyramidion
A triangle containing a semicircle and an equilateral triangle. What fraction is golden?
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Triple dice
An equilateral triangle with three congruent squares. What’s the angle α?
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Paper hat II
Two overlapping congruent right triangles. If |AB|=15 and |BC|=7, what is the total area?
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En garde
An isosceles triangle with two altitudes dividing each other in segments of length 4 and 5. What is the total triangle area?