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
Advanced

The Moroni minimum

An arbitrary point on the parabola y=x2. Shown are the tangent in that point and a line segment perpendicular to it. What is the minimal height h?

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

Family ties

Two regular pentagons share a vertex. What is the proportion red : green?

Categories
Intermediate

The seventh bell

A regular hexagon shares a vertex with an equilateral triangle of area 7. What is the area of the hexagon?

Categories
Beginner

Longing for spring

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

Categories
Advanced

The common ground

Two squares share a vertex. Two other vertices are 4 units apart. A third green square has the centres as opposite vertices. What is its area?

Categories
Intermediate

Rising bread

A regular hexagon with a diagonal and a circular arc centred in a side midpoint. What fraction is yellow?