MathDB

Easy geometry: r^2=xyz/(x+y+z)

Source:

April 16, 2012

geometryinradius

Problem Statement

Suppose

ABC

is a triangle with inradius

r

. The incircle touches the sides

BC, CA,

and

AB

D,E

and

F

respectively. If

BD=x, CE=y

and

AF=z

, then show that

r^2=\frac{xyz}{x+y+z}