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Intersection between Secants

Two chords AP...

Question

Two chords AP and QM of a circle intersect internally at a point R. If AR = 14 cm, RP = 9 cm, and RQ = 21 cm, then find MR.

A

2 cm

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B

4 cm

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C

6 cm

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D

9 cm

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Solution

The correct option is C
6 cm

When two chords of a circle intersect internally, then the products of the lengths of segments are equal.

i.e. $A R \times R P = M R \times R Q \Rightarrow 14 \times 9 = M R \times 21 \Rightarrow \frac{14 \times 9}{21} = M R$
$∴$ MR = 6 cm

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