Categories
Beginner

The guylines

Two squares and an extended side. What’s the angle α?

Categories
Advanced

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?

Categories
Intermediate

Know all angles

A triangle with its circumcircle and circumcentre. What’s α : β?

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

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?