Let ΔABC be an equilateral triangle, and construct its incircle (circle tangent to the &#3...

Let ΔABC be an equilateral triangle, and construct its incircle (circle tangent to the ' sides of ΔABC, with center at the point of intersection of the angle bisectors).

Locate P on this circle, and measure x, y, and z, as shown in the figure. Investigate the maximum/minimum properties of

(a) x + y + z

(b) x2 + y2 + z2