Categories
Beginner

True colours

In this right triangle, if red = blue, what is orange : purple?

Categories
Intermediate

We are equal

A quadrilateral with its diagonals. What’s the angle α?

Categories
Intermediate

A nice percentage

An orange square and a blue rectangle with two congruent inscribed circles. What is the angle α?

Categories
Intermediate

The gremlin

Two circles and three coloured isosceles triangles. Prove that the circles are concentric.

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
Beginner

The chain

Three semicircles and a circle. Three centres are shown in green. What’s the proportion red : blue?

Categories
Intermediate

Sliding down

Two squares share a vertex. One line segment connects their centres, another two vertices. What is the length proportion blue : red?

Categories
Intermediate

The wall socket

Two equilateral triangles share a vertex. Prove that their centres and the highlighted vertex are collinear.

Categories
Beginner

The remote corner

A square and a circle. What is the green area?

Categories
Advanced

The sneak peek

A rectangle with given side lengths is folded back and forth such that the corner touches the opposite side as shown. What is the minimal shaded fraction?