Multiple choice

PQ and RS are two chords of a circle. When PQ and RS are produced, they meet at M. If MR = 5.6 cm, QM = 6.3 cm and PQ = 7.7 cm, then find the length of RS?

  1. 9 cm

  2. 9.25 cm

  3. 8.35 cm

  4. 10.15 cm
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

For two chords PQ and RS of a circle extended to meet at M, the power of point theorem states: MQ·MP = MR·MS. Given MR = 5.6 cm, QM = 6.3 cm, and PQ = 7.7 cm. We have MP = MQ + QP = 6.3 + 7.7 = 14 cm. So MQ·MP = 6.3 × 14 = 88.2. This equals MR·MS = 5.6 × MS, so MS = 88.2/5.6 = 15.75 cm. Therefore RS = MS - MR = 15.75 - 5.6 = 10.15 cm.

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