Categories
Intermediate

The wall socket

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

Categories
Intermediate

Fair and square

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

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’?

Categories
Beginner

Three folds

A square divided by three line segments. What’s the proportion yellow : purple?

Categories
Beginner

Opposing camps

A square containing two overlapping equilateral triangles. What’s the length proportion a : b?

Categories
Advanced

Spiegel im Spiegel

A triangle with an inscribed triangle. What fraction of the former does the latter cover in terms of lengths a, b, c, d, e and f?

Categories
Beginner

The lever of Archimedes

Two congruent triangles are placed as shown. A line segment passes through the centroid of the yellow triangle. What’s the proportion a : b?

Categories
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?