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Question

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

A
2:1
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B
1:2
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C
1:1
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Solution

The correct option is C 1:1
Consider the above circle where OM is given to be perpendicular to AB.
Then, OMA=OMB=90.
Also, OA = OB = radius of the circle.
And, OM = OM (Common).
Thus, by RHS congruency criterion, OMAOMB.
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.

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