Question

AB is a diameter of a circle .AH and BK are perpendiculars from A and B respectively to the tangent at P .Prove that AH + BK= AB

Answer 1

According to question

Let O be the center of the circle and join O to P

Thus OP = radius of the circle = r

we  are given that     AB =  diamete

So  AB / 2 = Radius = r = OP

Also   OP  = AH = BK
So
AB / 2 = AH
AB = 2 AH
AB = AH + BK

Hence Proved