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?

Middle Man

Age 16 to 18 Challenge Level

Mark a point $P$ inside a closed curve.

Is it always possible to find two points that lie on the curve,
such that $P$ is the mid point of the line joining these two
points?