Categories
Intermediate

Fair and square

Two squares of which three vertices form an isosceles triangle. What is the angle α?

Categories
Advanced

The golf ball

A circle and a triangle with two sides tangent to the circle and a side connecting the tangency points. The line segment of the circle centre to the triangle apex is shown. Prove that α = β.

Categories
Intermediate

Égalité

A square with its diagonal and a circle. If red is equal to blue, what’s the angle α?

Categories
Intermediate

The bungee cords

Three squares and two line segments. What’s the angle α?

Categories
Beginner

The pentagon attack

Two regular pentagons and two diagonals. What’s the angle α?

Categories
Beginner

Lean on me

Two squares and two diagonals. Prove that the angles α and β are equal.

Categories
Advanced

Twin balls

A semicircle with two inscribed circles tangent to an altitude. What’s the angle α?

Categories
Beginner

The French kiss

Two tangent circles and two red tangent line segments. The three tangency points are shown. What is the angle β in terms of the angle α?

Categories
Beginner

The Gouda cheese

A quarter circle with two inscribed squares. What’s the angle α?

Categories
Beginner

The glass piece

A square and an overlapping isosceles triangle. What is the angle α?