In Δ ABC, m∠A = 90, is an altitude. So AB² = ……

By Pythagoras Theorem in ΔABD,

AB² = AD² + BD² ...... (1)

As we know that,

If an altitude is drawn to hypotenuse of a right angled triangle, then the length of altitude is the geometric mean of lengths of segments of hypotenuse formed by the altitude.

AD² = BD.CD ...... (2)

From equation (1) and (2)

AB² = BD.CD + BD²

⇒ AB² = BD(CD + BD)

⇒ AB² = BD.BC

∴ Option (a) is correct.