Try this Drag any orange dot. The angle ∠QRP will always be a right angle.
Put another way: If a triangle has, as one side, the diameter of a circle, and the third
vertex of the triangle is any
point on the circumference of the circle,
then the triangle will always be a right triangle.
In the figure above, no matter how you move the points P,Q and R, the triangle PQR is always a
right triangle, and the angle
∠PRQ is always a right angle.
A practical application - finding the center of a circle
The converse of Thales Theorem is useful when you are trying to find the center of a circle.
In the figure on the right, a
is on the circle always "cuts off" a diameter of the circle. That is,
the points P and Q are always the ends of a
Since the diameter passes through the center, by drawing two such diameters the center is found at the point where the diameters