A cone has height 6 and base diameter 6. On it lie two points, one exactly halfway up, the other diametrically opposed at the base. What’s the shortest distance between these points going along the cone surface?
A spider situated at point A on the outside of a cylinder with diameter 4 and height 3 is trying to get to a fly at point C on the complete opposite side as fast as possible. What is the shortest route?
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?
A square and a half square are stacked in order to form a house-shaped quadrilateral. Inside two circles are closely packed. What’s the angle between the tangency points?
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