In a square, an interior point is drawn with an angle to the top vertices of 120°. What’s the angle between the chords formed by the two arcs centered in these vertices?
Two squares and two equilateral triangles. What fraction is hatched?
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?
A wheel is placed inside another that has exactly twice its radius. If the inner wheel rolls around once without slipping, how many revolutions has it completed?
A square is divided into triangles and quadrilaterals as shown. What fraction of the square area is covered by the shaded triangle?
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?
On two faces of a cube a diagonal is drawn that meet in the same vertex. What’s the angle between them?
Four congruent rectangles are placed in a hat-shaped configuration. What’s the angle between the lines connecting the opposite corners?
A snooker player wants to corner a ball starting from a point on one side and bouncing two times from the opposite sides. Given the dimensions of the table in the figure, what’s the length of the track the snooker ball travels?
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?