Question

The perpendicular drawn from the centre of the circle to a chord divides the chord in the ratio .

• A. 2:1
• B. 1:2
• C. 1:1

Answer 1

The correct option is C 1:1

Consider the above circle where OM is given to be perpendicular to AB.
Then, $\angle OMA=\angle OMB={90}^{\circ }.$
Also, OA = OB = radius of the circle.
And, OM = OM (Common).
Thus, by RHS congruency criterion, $△OMA\cong △OMB.$
$⟹AM=BM$ by C.P.C.T.
In other words, the perpendicular drawn from the centre of a circle to a chord bisects the chord.
i.e., the perpendicular drawn from the centre of a circle to a chord divides the chord in the ratio 1:1.