Two equilateral triangles share a vertex. Prove that their centres and the highlighted vertex are collinear.
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The wall socket
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The remote corner
A square and a circle. What is the green area?
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The sneak peek
A rectangle with given side lengths is folded back and forth such that the corner touches the opposite side as shown. What is the minimal shaded fraction?
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Fair and square
Two squares of which three vertices form an isosceles triangle. What is the angle α?
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The double helix
Five equidistant parallel line segments. What’s the proportion green : red?
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The push-up
Two squares share a vertex. What’s the proportion x : y in terms of side lengths a and b?
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The glass ceiling
Three squares, two of which share a vertex. What is the total area?
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The golf ball
A circle and a triangle with two sides tangent to the circle and a side connecting the tangency points. The line segment of the circle centre to the triangle apex is shown. Prove that α = β.
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The triangle pull
An equilateral triangle with given distances between its vertices and an exterior point. What’s its side length x?
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The rotary movement
Two arbitrarily placed congruent equilateral triangles. Out of all the possible rotations of the plane, for how many will the image of ABC be A’B’C’?