Sitting Pretty
Sitting Pretty printable sheet
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 $\dfrac{1}{r} = \dfrac{1}{x} + \dfrac{1}{y}$.
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