Let X be a point in the interior of triangle PQR.
Let a line through X intersect rays QP and QR in points A and B respectively.
Let Y be the point on line segment AB such that BY = AX.
Prove that AB is a minimum if and only if AB is perpendicular to QY.
(In reply to
re(2): minimum? by Dej Mar)
Playing around with Geometer's Sketchpad, with an arbitrary point X within an arbitrary triangle, and a line is created going through X, and point Y constructed to fit the description, when the line going through point X is swiveled around and the measure of line AB is made to be at a minimum, it is indeed found that the newly recalculated Y is in a position such that QY is perpendicular to AB.

Posted by Charlie
on 20070510 12:29:17 