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?

# Category: Intermediate

## Sharing is caring

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

## Lopsided

The apex of a parabola is the shared vertex of two rectangles. Proof that the rectangles are similar.

## Harmonic proportions

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

## The piercing

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

## The crazy quilt

A parallelogram is divided into several areas. What is the area X of the blue trapezium?

## The common focus

A parabola, its symmetry axis and a tangent. Yellow connects the focus to the intersection point. Red connects the focus to the tangency point. What’s yellow : red?

## 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?

## The queen

A cyclic quadrilateral with extended sides and two tangents forming an angle γ. What is γ in terms of α and β?