Multiple choice

The length of the common chord of two circles of radii 30cm. and 40cm. whose centres are 50 cm. apart, in (in cm.) त्रिज्या 30 सेमी. और 40 सेमी. वाले दो वृत्तों की उभयनिष्ठ जीवा की लम्बाई, जिनके केन्द्र 50 सेमी. दूरी पर हैं, (सेमी. में)

  1. 12

  2. 24

  3. 36

  4. 48
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D Correct answer
Explanation

For two intersecting circles with radii r1=30, r2=40 and distance d=50, the common chord length = 2 × √(r1² - (d² + r1² - r2²)²/(4d²)). Using this formula or noting that 30-40-50 is a right triangle, the perpendicular distance from centers to chord gives chord length = 48 cm.

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