The shortest path between any two points on a snooker table is the straight line between them but what if the ball must bounce off one wall, or 2 walls, or 3 walls?

Three equilateral triangles ABC, AYX and XZB are drawn with the
point X a moveable point on AB. The points P, Q and R are the
centres of the three triangles. What can you say about triangle
PQR?

Four Points on a Cube

Age 16 to 18 Challenge Level

Take a cube of side length one unit. A vertex of the cube and
the centres of the three faces not containing that vertex form the
vertices of a tetrahedron. What is the surface area of this
tetrahedron?