COMC 2011 Problem 9
Source:
November 4, 2012
analytic geometrygraphing linesslopegeometrycircumcircle
Problem Statement
ABC is a triangle with coordinates A =(2, 6), B =(0, 0), and C =(14, 0).
(a) Let P be the midpoint of AB. Determine the equation of the line perpendicular to AB passing through P.
(b) Let Q be the point on line BC for which PQ is perpendicular to AB. Determine the length of AQ.
(c) There is a (unique) circle passing through the points A, B, and C. Determine the radius of this circle.