91Ó°ÊÓ

Show that in a quadrilateral circumscribed about a circle, the sum of the lengths of a pair of opposite sides equals the sum of the lengths of the remaining pair of opposite sides.

Find the radius, \(\mathrm{r}\), of the inscribed circle of right triangle \(\mathrm{ABC}\) in terms of leg lengths a and \(\mathrm{b}\) and hypotenuse length \(\mathrm{c}\).