If you roll a circle down a parabola, small circles can roll all the way down and up, whereas large circles get stuck between the sides at some point. What is the transition radius? In other words, what’s the maximum circle that keeps on rolling?
A semicircle and an interior circle are tangent to each other. The chord towards the tangency point is divided in segments of length 1 and 2. What is the pink area?
A triangle with a quadrilateral that covers half its area. What is the angle?
A point lies 8 from the centre of a circle of radius 6. The angle α is variable. What’s the maximum triangle area?
Three squares. The top line segment is variable in length. What’s the minimal blue fraction?
Don Quixote is approaching a windmill. The sails of length √2 are attached to a point that is 2 above eye level. What is the maximum vertical angle that Don Quixote perceives as he moves forward?
Two squares share a vertex. An isosceles triangle connects three others. What fraction is blue?
Two congruent squares inside a circle. The extended diagonals meet at the circle circumference. What’s their angle?
A quarter circle containing two touching semicircles cut by a chord. What fraction is brown?
Three touching congruent circles inscribed in an equilateral triangle. A small equilateral triangle inscribed in the centre space. What fraction is blue?