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
Intermediate

The radical

Two intersecting circles and a common tangent. The two tangency points are shown in black. Prove that the three red points are collinear.

Categories
Intermediate

Getting stuck

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

Categories
Beginner

The dirty thirties

A triangle containing a semicircle and a circular sector centred in the right vertex. What is blue : green?

Categories
Intermediate

Scratching the surface

Three tangent semicircles and two coloured triangles. What’s the proportion yellow : green?

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
Beginner

Longing for spring

Four semicircles and three line segments. What’s the proportion yellow : orange?

Categories
Advanced

Çetins circle

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

Categories
Intermediate

Mother and child

Two circles, two radii and three chords. What is the length of radius x in terms of a, b and c?

Categories
Intermediate

The side mirror

An isosceles triangle and an external point with three line segments. Prove that the red points form a cyclic quadrilateral.