A triangle containing a semicircle and a circular sector centred in the right vertex. What is blue : green?

# Tag: circle

## Scratching the surface

Three tangent semicircles and two coloured triangles. What’s the proportion yellow : green?

## To the core

A non-isosceles triangle with a red cevian and three line segments to a point on the cevian. Prove that this point is the incentre of the triangle.

## Longing for spring

Four semicircles and three line segments. What’s the proportion yellow : orange?

## Çetins circle

A square, a semicircle and six line segments. What’s the angle α?

## Mother and child

Two circles, two radii and three chords. What is the length of radius x in terms of a, b and c?

## The side mirror

An isosceles triangle and an external point with three line segments. Prove that the red points form a cyclic quadrilateral.

## Uneven cups

Two semicircles and several line segments. Prove that the red line segments are parallel.

## The triskelion

A circle containing an equilateral triangle and three squares. What fraction is purple?

## Ruyles squares

There are four possible squares with a vertex at distance a from the centre and two vertices on the circle of radius r. Find their areas in terms of a and r.