In triangle ABC, bisector AE is drawn, AB = BC BC = 6, AC = 8. Find BE and EC.

By the property of the bisector of the angle of a triangle, the bisector divides the opposite side into segments proportional to the adjacent sides.

By the condition AB = BC = 6 cm.

Let the segment BE = X cm, then CE = (BC – X) = (6 – X) cm.

Then:

BE / AB = CE / CA.

X / 6 = (6 – X) / 8.

36 – 6 * X = 8 * X.

14 * X = 36.

X = 36/14 = 18/7 = 2 (4/7) cm.

BE = 2 (4/7) cm.

CE = 6 – 2 (4/7) = 24/7 = 3 (3/7) cm.

Answer: BE = 2 (4/7) cm, CE = 3 (3/7) cm.