The Incircle of a Triangle A circle is called the incircle of a triangle iff it is tangent...

The Incircle of a Triangle A circle is called the incircle of a triangle iff it is tangent to all three sides (and accordingly, lies inside the triangle). The radius and center of the incircle are called the inradius, denoted r, and incenter, denoted I.

(a) Prove that the incircle exists for ∆ABC. (See Problem 12, Section 3.6.)

(b) Show that, in standard notation, and with semiperimeter s = (a + b + c), the measures x, y, and z in the figure are given by

*See Problem 9, Section 4.8.