Multiple choice

Two circle C (O, r) and C' (O', r1) intersect each other at P and Q respectively. OO' cut common chord at M such that OQ = 17 cm and OM = 15 cm then find the length of PQ. दो वृत्त C (O, r) और C' (O', r1) एक दूसरे को बिन्दु P और Q पर प्रतिच्छेद करते हैं रेखा OO' उभयनिष्ठ जीवा PQ का M पर इस प्रकार प्रतिच्छेद करती है कि OQ = 17 सेमी और OM = 15 सेमी. तो PQकी माप ज्ञात कीजिए।

  1. 8 cm/ सेमी.

  2. 12 cm/ सेमी.

  3. 20 cm/ सेमी.

  4. 16 cm/ सेमी.

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D Correct answer
Explanation

OO' is the perpendicular bisector of common chord PQ. Triangle OMQ is right-angled at M. OQ = 17 cm (radius), OM = 15 cm (distance from center to chord). Using Pythagoras: PM² = OQ² - OM² = 17² - 15² = 289 - 225 = 64, so PM = 8 cm. Since M is midpoint of PQ, total PQ = 2 × PM = 16 cm.