XAT 2017 Question 49
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XAT
Let us draw the diagram using the given conditions.
AB = 24 cm and P is the mid-point of AB. Therefore, AP=PB=12 cm.
MN is perpendicular to AB and passes through P.
PM < PN. Therefore, M should be closer to A and B than N.
MN and AB are 2 perpendicular chords intersecting at P.
Therefore, according to the intersecting chords theorem, AP*PB = PM*PN
12*12=8*PN
=> PN = 18 cm.
Therefore, option B is the right answer.