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Three Balls

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

Chris, age 15, was able to solve the first part:

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.