Categories
Beginner

The movie film

Four squares and two shared vertices. What fraction is blue?

Categories
Intermediate

An irregular tiling

A triangle divided by three line segments. What fraction is blue?

Categories
Beginner

The guylines

Two squares and an extended side. What’s the angle α?

Categories
Intermediate

Cross the line

An equilateral triangle with two line segments crossing exactly on the semicircle. What is the proportion red : green?

Categories
Intermediate

The baby block

Two squares and an extended side. Prove that red : green = blue : yellow.

Categories
Beginner

The England win

A unit square containing two red overlapping congruent rectangles. If they cover exactly half the square’s area, what is their width x?

Categories
Intermediate

A fair division

A square with a diagonal and a right triangle. What’s the proportion blue : red?

Categories
Intermediate

The steam locomotive

Two tangent circles, a chord towards the tangency point and a tangent. What’s the proportion a : b in terms of radii R and r?

Categories
Advanced

The inner circle

A triangle with its incircle. A line segment through two tangency points and one through the incentre. What’s the angle α?

Categories
Intermediate

Know all angles

A triangle with its circumcircle and circumcentre. What’s α : β?