Date: Dec 27, 1997 10:13 PM
Author: Eileen Stevenson
Subject: to prove: rays bisecting 3 angles of a triangle meet at a single point
I have a geometry puzzle that I cannot seem to prove.
I believe that if you bisect each of the 3 angles of a triangle with 3
rays, those rays will meet at a single point.
But I can't prove it. Can anyone help?
( related: there are 2 other interesting points determined by a triangle:
1. The center: If you bisect a side of a triangle & draw a line
passing through the bisecting point and the oposite corner of the triangle,
then do the same with the other 2 sides, all three will intersect at a
single point, the center of the triangle. This is generally NOT the same
point as I am asking about above.
2. The center of the circle defined by the triangle. 3 points
determine a circle. If you bisect the 3 sides with perpendicular lines,
they will meet at a point that determines the center of the unique circle
specified by the triangle.
I can prove these 2, & will if anyone cares, but not my first queston.
Any help is appriciated.