A parabola passing through a square’s bottom vertices and tangent to its top side. What fraction is blue?
Author: Rik D. Tangerman
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.
The giant’s shoulder
Two equilateral triangles inside a square. What’s the proportion orange : blue?
Buddha’s belly
A square containing a quarter circle and a tangent line segment. What is a : b?
The bubble chamber
A regular hexagon and two semicircles connecting vertices. What’s the angle α between the chords?
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?
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?
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?
The Queen’s chamber
A right triangle with three squares forming a smaller inner triangle. What is the maximal blue fraction?
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.