ANGLE BISECTORS An angle bisector of a triangle is a cevian that divides a vertex angle into two congruent angles and intersects the opposite side. Every triangle has three angle bisectors. They intersect inside the triangle at a point called the incenter. The incenter is also the center of the triangle's inscribed circle, or incircle. B ANGLE BISECTOR THEOREM: The angle bisector of a triangle divides the opposite side into two segments that are proportional to the other two sides of the triangle. Triangle ABC, shown here, F has angle bisectors AD, BE and CF with the following proportions: D AB BD AB AE AC AF A C E AC CD BC CE BC BF P 28. cm Triangle POR has angle bisector PS, as shown, with PQ = 16 cm, RS = 11 cm and QS = 8 cm. What is the perimeter of triangle POR? 16 Q R 8 S 11 A 29. Triangle ABC has angle bisectors AD, BE and CF, as shown, and AB = 10, F E BC = 7, AC = 11. What is the ratio of DG to AG? Express your answer as a KG common fraction. B C D D B