Question

1. In the figure, OD is perpendicular to chord AB of a circle whose centre is O. If BC is a diameter; prove that CA = 2OD.

Answer 1

SOLUTION:-

Given:

OD is perpendicular to chord AB of a circle where centre is O. BC is a diameter of the circle.

To prove:

CA = 2OD.

Proof:

OD Perpendicular to AB [given]

D is the midpoint of AB.

[The perpendicular drawn from the centre of a circle to a chord bisects the chord]

&

In ∆BAC,

D is the midpoint of AB & O is the midpoint of BC.

OD||AC by midpoint theorem

So,

OD = 1/2AC

=) CA = 2OD

Hence,

Proved.