Two circles and three coloured isosceles triangles. Prove that the circles are concentric.
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The gremlin
Category: Intermediate
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Sliding down
Two squares share a vertex. One line segment connects their centres, another two vertices. What is the length proportion blue : red?
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The wall socket
Two equilateral triangles share a vertex. Prove that their centres and the highlighted vertex are collinear.
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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 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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Seeing double
Five circles, of which the green circles are congruent and so are the blue ones. If rblue : rgreen= 6, what’s rred : rgreen?
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Égalité
A square with its diagonal and a circle. If red is equal to blue, what’s the angle α?
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House of Orange
A right triangle with a red and yellow square attached. Two circular arcs centered in the triangle vertices. What is the area of the orange rectangle in terms of red and yellow?