COMC 2011 C Problem 1

A B C is a triangle with coordinates A=(2,6), B=(0,0), and C=(14,0).

(a) Let P be the midpoint of A B. Determine the equation of the line perpendicular to A B passing through P.

(b) Let Q be the point on line B C for which P Q is perpendicular to A B. Determine the length of A Q.

(c) There is a (unique) circle passing through the points A, B, and C. Determine the radius of this circle.