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?

# Tag: proportion

## Sharing is caring

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

## Harmonic proportions

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

## 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?

## The purple hat

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

## The Pisa experiment

Four squares and an altitude to the top vertex form a right yellow traingle. What is the proportion yellow : green?

## The parrot

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

## Two hemispheres

A triangle with its circumscribed circle and a smaller intersecting circle. The two intersection points and the circumcentre are shown. What’s the proportion red : green?

## Overhanging rock

A rectangle with three line segments. What’s the proportion red : yellow?

## Emerging from water

Two squares and an extended side. What’s red : green : pink?