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Intermediate

The wall socket

Two equilateral triangles share a vertex. Prove that their centres and the highlighted vertex are collinear.

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Intermediate

Fair and square

Two squares of which three vertices form an isosceles triangle. What is the angle α?

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Intermediate

The double helix

Five equidistant parallel line segments. What’s the proportion green : red?

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Intermediate

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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Intermediate

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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Intermediate

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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Intermediate

Égalité

A square with its diagonal and a circle. If red is equal to blue, what’s the angle α?

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Intermediate

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?

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Intermediate

Head above water

A unit square with an extended side immersed in another square. What is the area of the red triangle?

Categories
Intermediate

The framing effect

Four squares, three of which are coloured. What’s the area of the blue one?