A triangle with two cevians. What is d/c-b/a?

## 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?

## The chess board

A square is divided by six line segments. What fraction is brown?

A unit circle with an inscribed square and four semicircles. What’s the sum of the semicircle areas?

## The Olympic bowl

A parabola is tangent to the equal sides of an isosceles triangle in its equal vertices. Another tangent is drawn as shown. Prove that the red line segments are congruent.

## As above, so below

A semicircle, a square, a triangle and two circles. A centre and a tangency point are highlighted. Prove that the circles are congruent.

## Down to earth

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

## The sand heap

Two squares share a vertex. Three other vertices form a triangle, of which one side length is given. What is its area?