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, △OMA≅△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.