CAT 2017 Geometry & Mensuration Question (Medium)

Question

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 meet the circle at M and N respectively. If PM PN and PM 8 cm, then what will be the length of PN?

Optima Learn · Accepted Answer

Let the radius of the circle be R and the distance of the centre from P along the perpendicular be d. Since PM PN, we have PM R d 8 R 8 d. Also, since AB 24, half-chord 12, so by geometry R 12 d . Hence 8 d 144 d 64 16d 144 d 5, so R 13. Therefore PN R d 13 5 18 cm.

CAT 2017 Geometry & Mensuration — Previous Year Question

CAT 2017

Quantitative

Geometry & Mensuration

Medium

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