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## 'Sitting Pretty' printed from http://nrich.maths.org/

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 $y$.

Show that

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