Question

The perpendicular drawn from centre to the chord bisects the chord for a circle.

• A. True
• B. False

Answer 1

The correct option is A True

Given :

A chord PQ of a circle C(O,r) and perpendicular OL to the chord PQ.

To Prove :

$LP=LQ$

Construction :

Join OP and OQ.

Proof :

In triangles PLO and QLO,

$OP=OQ=r$

$OL=OL$

$\angle OLP=\angle OLQ$

So, by RHS-criterion of congruence,

$△PLO\cong △QLO$

$PL=LQ$

Hence, proved.

Thus, the given statement is true.