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

# Tag: triangle

## 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?

## Sharing is caring

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

## Harmonic proportions

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

## The parallax effect

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

## The piercing

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

## The purple hat

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

## The bell tolls

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

## Under the volcano

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

## The Pisa experiment

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