ABC is a right-angled triangle with angle B = 90°. A circle with BC as diameter cuts the hypotenuse AC at Point P. AB = 15 cm and BC = 8 cm. What is the distance from the point P to vertex A?

In right triangle ABC with angle B = 90°, AB = 15 cm and BC = 8 cm, the hypotenuse AC = sqrt(15² + 8²) = sqrt(225 + 64) = sqrt(289) = 17 cm (by Pythagorean Theorem). A circle with BC as diameter passes through point P on AC. By Thales' theorem, angle BPC = 90°. Triangle BPC is similar to triangle ABC, giving the ratio CP/BC = BC/AC. Solving: CP = 8²/17 = 64/17 ≈ 3.76 cm. Therefore AP = AC - CP = 17 - 3.76 = 13.24 cm ≈ 13.2 cm.