Let circle A be in the interior of circle B and tangent to it at point M. Let chord QR of circle B be tangent to circle A at point P. Prove that angles PMQ and PMR are equal.

1993 British Mathematical Olympiad,Round 1,Problem 4.

It doesn't really matter what the centre of the circle is called!!!

Yes, N is on the circumference, MN is a diameter and since M & P are also on the circumference we have the angle subtended by RN the same at each point.

Posted by DrBob on 2005-12-15 10:42:25