Multiple choice

AB is a chord of the circle with centre O, such that OP is perpendicular to AB and OP intersect AB at point M. If AB = 8cm, MP = 2cm then find the radius of the circle O केंद्र वाले वृत्त की जीवा AB इस प्रकार है कि OP, AB पर लम्ब है और OP ,AB को बिंदु M पर प्रतिच्छेदित करता है .यदि AB=8 सेमी ,MP=2 सेमी तो वृत्त की त्रिज्या ज्ञात कीजिए |

  1. 7 cm / सेमी

  2. 5 cm / सेमी

  3. 4 cm / सेमी

  4. 6 cm / सेमी

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B Correct answer
Explanation

In the circle, OM is perpendicular to chord AB. M is midpoint of AB, so AM = MB = 4 cm. Let OM = d. In right triangle OMA: OA² = OM² + AM² = d² + 16 = r². Given MP = 2 cm. Since OM + MP = OP = r (if P lies on radius extended), we have d + 2 = r. Substituting: r² = (r-2)² + 16 = r² - 4r + 4 + 16, giving 4r = 20, so r = 5 cm.