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Question 49
AB is a chord of a circle. The length of AB is 24 cm. P is the midpoint of AB. Perpendiculars from P on either side of the chord meets the circle at M and N respectively. If PM < PN and PM = 8 cm. then what will be the length of PN?
Solution
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.
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.
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