Stage: 4 Challenge Level:
Chris, age 15, was able to solve the first
As $OP$ is a radius and $PT$ is a tangent, the angle between them
is a right angle. So the triangle $OPT$ is right angled, and the
hypotenuse is the diameter of the circle, so $P$ lies on the
circle. In the same way, $Q$ lies on the circle.