Multiple choice

In a circle of radius 10 cm and center O, PQ and PR are two equal chords, each of length 12 cm. find the length of chord QR (in cm).

  1. 19.2

  2. 20.5

  3. 17.8

  4. 14.2
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A Correct answer
Explanation

PQ = PR = 12 cm, radius = 10 cm. Drop perpendicular from O to PQ, meeting at M. OM = √(10² - 6²) = 8 cm. Since PQ = PR, triangles PQM and PRM are congruent. ∠QPR = 2arcsin(6/10) ≈ 73.74°. Using law of cosines in triangle PQR: QR² = 12² + 12² - 2(12)(12)cos(73.74°) ≈ 288 - 288(0.28) ≈ 207.36, so QR ≈ 19.2 cm.

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