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. tia.