In the given figure, If O is the centre of the circle and the minor arc corresponding to chord MN is equal to the minor arc corresponding to chord PQ, then which of the following is true?

ML = QR

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NL < QR

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ML > PR

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NL > PR

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Solution

The correct option is A ML = QR
Given that the minor arcs corresponding to chords MN and PQ are equal, we have:
MN = PQ (Equal arcs of a circle cut equal chords,)...(i)

Since OL $⊥$ PQ, we have:
ML = NL ...(ii) and PR = QR...(iii)
(A straight line from the centre to a chord and perpendicular to it bisects it.)

From (i), (ii) and (iii), we get ML = NL = PR = QR
Thus, ML = QR,

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