A square containing a quarter circle and a red equilateral triangle. What’s the orange fraction?

# Category: Beginner

A regular hexagon, a square with its diagonals, an equilateral triangle and a circle. Prove that the hexagon and the circle are concentric.

## The common triangle

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

## The fried egg

Two concentric circles and two tangents. What is the yellow fraction?

## The parallax effect

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

## The purple hat

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

## The parrot

Two squares, a diagonal and a line segment. What is red : blue : green?

## The leftward lean

Two triangles form a quadrilateral. What’s the total orange area?

## The green deal

Three squares, one of which has a side length of 2. What is the green area?

## The high seas

A rectangle containing four triangles. What is the total area?