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Equal Chords Are at Equal Distances from the Center

Chords MN and...

Question

Chords MN and RS of a circle intersect at P outside the circle. If $P N = 3 c m, M N = 5 c m, P R = 2 c m$ , then the value of SR is equal to

5 cm

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8 cm

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15 cm

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10 cm

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Solution

The correct option is D 10 cm
We know that,
$P N \times P M = P R \times P S$

On putting the values, we get
$3 \times (3 + 5) = 2 \times (2 + S R)$
$3 \times 8 = 2 \times (2 + S R)$
$24 = 2 \times (2 + S R)$
$2 + S R = 12$
$S R = 10 c m$

Hence, this is the answer.

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