Question

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

• A. 2 cm
• B. 4 cm
• C. 6 cm
• D. 9 cm

Answer 1

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. $AR\times RP=MR\times RQ\Rightarrow 14\times 9=MR\times 21\Rightarrow \frac{14\times 9}{21}=MR$
$\therefore$ MR = 6 cm