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.
Black hole sun
A square containing two quarter circles and a common tangent. What is the proportion yellow : black?
My two cents
A right triangle is divided in two triangles, one of which is isosceles. The two inscribed circles are congruent. What is the total area?
The life net
The vertices of a regular hexagon are connected to midpoints of opposing sides. What fraction is red?
The lunar twins
Three circles are tangent to each other. The black chords go through their tangency points. Prove that the red chord is a diameter of the largest circle.
Below the line
Two squares share a vertex at the origin and have their sides along the x- and y-axis. Two vertices lie on the line satisfying x+2y=c. What is the proportion purple : yellow?
The red planet
A semicircle with a chord and a line segment perpendicular to it. What is the total area in terms of lengths a and b?
The ocean view
Two squares of variable size share a vertex. What is the maximal blue fraction?