Segment AD is the bisector of triangle ABC, in which the angle C = 90, AB = 15 cm and AC = 12 cm, find BD and CD.

In the right-angled triangle ABC, we find the leg BC according to the Pythagorean theorem:
BC = √ (AB ² – AC ²);
ВС = √ (15 ² – 12 ²);
BC = 9 (cm).
The angle bisector of a triangle divides the opposite side in a ratio equal to the ratio of the two adjacent sides.
CD / DB = 12/15 = 4/5;
ВD = 5 parts;
CD = 4 pieces;
CB = 9 parts.
CD = CB * 4/9 = 4 cm;
BD = 9 * 5/9 = 5cm.
Answer: ВD = 5 cm, СD = 4 cm.