Two coloured squares inside a triangle inside a square of side length a. What is the length proportion a : b?
Elasticity
Four squares and two triangles. Prove that the two green angles are congruent.
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.
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.
The Transamerica Pyramid
Two squares inscribed in a triangle. What fraction of its area is coloured?
The three day stubble
A regular pentagon and a square share two vertices. What’s the angle α?
It’s complicated
A circle, a semicircle and several triangles. The black points are tangency points. What proportions have the line segments a : r : b?
The odd couple
A semicircle with two inscribed triangles The tangency points of the incircle of the bigger triangle are shown. What is the triangle area proportion orange : blue?
Parallel universes
Two straight lines are specified by y=a+cx and y=b+cx, respectively, where b≥a. What’s the distance d between them in terms of a, b and c?
Blazing hot
A circle inscribed in a triangle inscribed in a semicircle. The line segment through two tangency points meets a radius at the semicircle circumference. What is the angle α?