XAT 2017 — QA & DI Question 4
Basics of CirclesEasy
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?
Answer & solution
- A
17 cm
18 cm
- C
19 cm
- D
20 cm
- E
21 cm
Solution
Let us draw the diagram using the given conditions.
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AB = 24 cm and P is the mid-point of AB.
∴ AP = PB = 12 cm.
MN is perpendicular to AB and passes through P.
PM < PN.
∴ 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.
Hence, option (b).