Three tangent semicircles and two coloured triangles. What’s the proportion yellow : green?

# Category: Intermediate

## To the core

A non-isosceles triangle with a red cevian and three line segments to a point on the cevian. Prove that this point is the incentre of the triangle.

## The seventh bell

A regular hexagon shares a vertex with an equilateral triangle of area 7. What is the area of the hexagon?

## Rising bread

A regular hexagon with a diagonal and a circular arc centred in a side midpoint. What fraction is yellow?

## The antenna

A regular pentagon with an extended side. What’s the angle α?

## The erratic spider

A square with several line segments. Prove that the blue ones are parallel.

## Black and blue

A square with an extended side inside another square. What fraction of the latter is blue?

## Mother and child

Two circles, two radii and three chords. What is the length of radius x in terms of a, b and c?

## The side mirror

An isosceles triangle and an external point with three line segments. Prove that the red points form a cyclic quadrilateral.

## Two brotherly pines

Three triangles are glued together. The green ones are based on a common line. What’s the angle α?