A triangle divided by three line segments. What fraction is blue?
The guylines
Two squares and an extended side. What’s the angle α?
Cross the line
An equilateral triangle with two line segments crossing exactly on the semicircle. What is the proportion red : green?
The baby block
Two squares and an extended side. Prove that red : green = blue : yellow.
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?
A fair division
A square with a diagonal and a right triangle. What’s the proportion blue : red?
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?
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?
Know all angles
A triangle with its circumcircle and circumcentre. What’s α : β?
True colours
In this right triangle, if red = blue, what is orange : purple?