Question

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

Answer 1

SOLUTION:
[FIGURE IS IN THE ATTACHMENT]
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)]

HOPE THIS WILL HELP YOU..

Answer 2

see it is very very easy