Categories

## The root cause

A square and an equilateral triangle are divided in several polygons. What is the proportion yellow : blue?

Categories

## Round and pointy

A circle is inscribed in both a semicircle and a right triangle. The three tangency points are shown. What is the angle α?

Categories

## The emerging pattern

A square, a circle and its centre. Prove that the six red points are on one circle.

Categories

## And counting

A triangle containing an altitude and the inscribed circle. One tangency point is shown. The red line segments have equal length. What is the proportion of the triangle sides a : b : c?

Categories

## The holy number

An equilateral triangle and several line segments. What fraction is purple?

Categories

## Protection

Two coloured squares inside a triangle inside a square of side length a. What is the length proportion a : b?

Categories

## Elasticity

Four squares and two triangles. Prove that the two green angles are congruent.

Categories

## The miniature version

Two rectangles share a vertex. Two line segments connecting opposing vertices and the common side intersect in a single point. Prove that the rectangles are similar.

Categories

## Wheels in motion

Two tangent circles and a third circle touching the line segment connecting their centres in the tangency point. Prove that the red points (centre and two intersection points) are collinear.

Categories

## The Transamerica Pyramid

Two squares inscribed in a triangle. What fraction of its area is coloured?