Partition of right triangle

Triangle ABC is a right triangle of AB = 18 cm, AC = 24 cm and BC = 30 cm.

The points P and Q are points on the bisectors of angle B and angle C, respectively.

PQ is parallel to BC. PH and AB, QK and AC are vertical respectively. The area of pentagon AHPQK is half of the area of triangle ABC.

Find the length of PH and the length of PQ.

Answer