Categories
Intermediate

Pushing the boundary

Two equilateral triangles are placed side by side. What’s the proportion green : red?

Categories
Intermediate

The gyroscope

Two ellipses go through each others focal points. Prove that the focal points are the vertices of a parallelogram.

Categories
Advanced

The Pappus eggs

Three semicircles and a circle with their centres. Two orange ellipses with focal points in the semicircle centres (they share the middle one). Prove that their upper intersection point coincides with the circle centre.

Categories
Intermediate

The sliding ladder

A ladder seen from the side is sliding down a wall. Prove that a fixed point on the ladder traces part of an ellipse.