Segment AD-is the bisector of triangle ABC Find BD and DC if AB = 14 cm, BC = 20 cm, AC = 21 cm.

The bisector AD divides the side BC in the ratio in which the adjacent sides AB and AC are:

BD / DC = AB / AC;

DC = BC – BD;

BD / (BC – BD) = AB / AC;

BD * AC = (BC – BD) * AB;

BD * AC = BC * AB – BD * AB

BD * (AC + AB) = BC * AB;

BD = (BC * AB) / (AC + AB) = (20 * 14) / (21 + 14) = (20 * 14) / 35 = (20 * 2) / 5 = 8 cm.

Answer: 8 cm.