A triangle with an inscribed rectangle. What is the maximum red fraction?
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 point lies 8 from the centre of a circle of radius 6. The angle α is variable. What’s the maximum triangle area?
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 congruent circles and a common tangent. A triangle connecting tangency points and the upper intersection point. What angle α maximises its area?
A square and two congruent isosceles triangles with variable top angle. What is the maximum fraction shaded?
An isosceles triangle is inscribed in a semicircle with one side along the diagonal and the top vertex somewhere on the semicircle. What’s the maximum fraction shaded?