# In a Triangle the Bisectors Intersect

Submitted by Isoscel on Sun, 11/11/2007 - 16:16.

The three bisectors of any triangle intersect.

Let ABC be a triangle and AA_{1}, BB_{1} and CC_{1} be its bisectors. Then AA_{1}, BB_{1} and CC_{1} intersect in a point I.

Proof:

A point is on the interior bisector line of an angle if and only if the distances to the two sides of the angle are equal.

Let us use this property to show that interior angle bisectors pass by one point.Consider As we have IH=IF. As we have IH=IJ and so IF=IJ and I belongs to the interior angle bisector of