Categories
Beginner

The common triangle

Two semicircles contain a triangle. The centre of the right semicircle is shown. Prove that the triangle is isosceles.

Categories
Intermediate

At navel level

Two equilateral triangles share a vertex. The centre of the larger one is aligned with the midpoint of a side of the smaller one. What is green : red?

Categories
Intermediate

Sharing is caring

Three equilateral triangles and three shared vertices. What’s the proportion blue : green?

Categories
Intermediate

Harmonic proportions

A trapezium with its diagonals and a parallel line segment. Prove that yellow : purple = blue : red.

Categories
Beginner

The parallax effect

Two intersecting circles with a triangle that passes through their centres and an intersection point. What’s the angle α?

Categories
Intermediate

The piercing

An equilateral triangle containing a right triangle and a line segment. What fraction is pink?

Categories
Beginner

The purple hat

A circle with three tangents forming an isosceles triangle. Two tangency points are shown. What is the proportion green : red?

Categories
Advanced

The bell tolls

An equilateral triangle inscribed in a rectangle. What is its area X in terms of triangle areas A and B?

Categories
Intermediate

Under the volcano

A square containing a right isosceles and an equilateral triangle. What’s the angle α?

Categories
Intermediate

The Pisa experiment

Four squares and an altitude to the top vertex form a right yellow traingle. What is the proportion yellow : green?