Question

Which diameter of a circle p is a point on the semicircle ap bhm bhm perpendicular from a and b respectively to the tangent at p prove that ab + bc is equal to a b?

Answer 1

SOLUTION__☺️

Given:

AH and BK are perpendiculars drawn from A and B on tangent at P.

To Prove:AH + BK = AB

PROOF:

ABKH is a rectangle.(AH & BK are Perpendiculars.

AB = HK …..…….....(1)

[Opposite sides of rectangle are equal]

We know that, the lengths of tangents drawn from an external point to the circle are equal.

AH = HP ……............(2)

BK = PK ..….............(3)

Adding eq. (2) and (3),

AH + BK = HP + PK = HK

AH + BK = AB [from eq. (1)]