Two squares and a rectangle. What is area of the rectangle in terms of square sides a and b?

# Category: Intermediate

## Tomba La Bomba

Three regular hexagons inside a circle. Two shared vertices and five vertices on the circle. What’s red : green?

## The augmented chord

A circle with four chords. What is the length of line segment x in terms of lengths a and b?

## The last wave

A square containing a quarter circle, a semicircle and a circle. What is the proportion blue : green?

## The tightrope dancer

A circle containing an isosceles and two equilateral triangles. What is the proportion orange : blue?

## The hidden pyramid

A triangle with an inscribed equilateral triangle. If areas A and B add up to C, what are the proportions A : B : C?

## Down to earth

Two equilateral triangles share a vertex. What is the proportion red : green?

## The residue

A parabola is tangent to two sides of a square and to the hypotenuse of an isosceles triangle. The three tangency points are shown. What fraction of the square is green?

## Jingle bells

Two equilateral triangles share a vertex. What is the area of their overlap region?

## Lost in rotation

Four equilateral triangles inscribed in a fifth one. What fraction of the latter is coloured?