Categories
Intermediate

The sandal

A triangle with two angular bisectors. What’s the proportion blue : red?

Categories
Beginner

Sliding down II

A quarter circle and a square. What’s the angle α?

Categories
Intermediate

Meeting halfway

Two squares and three line segments. What’s the angle α?

Categories
Intermediate

A square deal

A regular hexagon and a square share a vertex. What’s the angle α?

Categories
Intermediate

The balloon incident

A circle with a red and a green tangent. The two tangency points are shown. Prove that the blue and red line segments are parallel.

Categories
Advanced

The new normal

Two equilateral triangles are placed as shown. Their centres are connected as well as their intersection points. What’s the angle α?

Categories
Intermediate

Getting stuck

A regular pentagon and a circle through two of its vertices and its centre. What’s the angle α?

Categories
Intermediate

To the core

A non-isosceles triangle with a red cevian and three line segments to a point on the cevian. Prove that this point is the incentre of the triangle.

Categories
Intermediate

The antenna

A regular pentagon with an extended side. What’s the angle α?

Categories
Advanced

Çetins circle

A square, a semicircle and six line segments. What’s the angle α?