Categories
Beginner

Arc de Triomphe

A parabola passing through a square’s bottom vertices and tangent to its top side. What fraction is blue?

Categories
Intermediate

The minor chord

Three chords meet at the same point on the circumference of the circle. A perpendicular line segment divides one of them in two parts of length a and b. Express the length of the smallest chord x in terms of a and b.

Categories
Beginner

The giant’s shoulder

Two equilateral triangles inside a square. What’s the proportion orange : blue?

Categories
Beginner

Buddha’s belly

A square containing a quarter circle and a tangent line segment. What is a : b?

Categories
Intermediate

The bubble chamber

A regular hexagon and two semicircles connecting vertices. What’s the angle α between the chords?

Categories
Advanced

The stuck boulder

A rectangle contains a circle wedged between two triangles. What is the circle radius in terms of triangle heights a and b?

Categories
Intermediate

The ball pool

A square having side length 12 contains a quarter, semi and full circle. The centres of the latter two are connected to the square’s centre to form a green triangle. What is it’s area?

Categories
Beginner

Square eyes

A square with four quarter circles of which the intersection points are the vertices of a yellow quadrilateral. What fraction of the total area is yellow?

Categories
Advanced

The Queen’s chamber

A right triangle with three squares forming a smaller inner triangle. What is the maximal blue fraction?

Categories
Beginner

The outsider

A circle with an inscribed regular pentagon, a square and a triangle. Prove that the point lies on the circumference of the circle.