Categories
Intermediate

The wall socket

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

Categories
Beginner

The remote corner

A square and a circle. What is the green area?

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Advanced

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?

Categories
Intermediate

Fair and square

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

Categories
Intermediate

The double helix

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

Categories
Intermediate

The push-up

Two squares share a vertex. What’s the proportion x : y in terms of side lengths a and b?

Categories
Beginner

The glass ceiling

Three squares, two of which share a vertex. What is the total area?

Categories
Advanced

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.

Categories
Intermediate

The triangle pull

An equilateral triangle with given distances between its vertices and an exterior point. What’s its side length x?

Categories
Advanced

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’?