Sitting Pretty

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

A circle 'sits' on a right-angled triangle, touches two sides of the triangle and has its centre on the hypotenuse of the triangle. The circle has radius r and the triangle has sides of length x and y.
Sitting PrettyShow that

$\frac{1}{r} = \frac{1}{x} + \frac{1}{y}.$



Published September 1999,November 2008,December 2008.