Multiple choice

The length of the common chord of two circles of radii 15 cm. and 20 cm. whose centres are 25 cm. apart is? (in cm.) 15 सेमी. और 20 सेमी. त्रिज्या वाले दो वृत्तों की एक उभयनिष्ठ जीवा की लम्बाई (सेमी. में) क्या है जिनके केन्द्रों की दूरी 25 सेमी. है?

  1. 15 cm./सेमी.

  2. 20 cm./सेमी.

  3. 24 cm./सेमी.

  4. 25 cm./सेमी.
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C Correct answer
Explanation

For two circles with radii 15 cm and 20 cm, and center distance 25 cm, note that 15² + 20² = 225 + 400 = 625 = 25², so the circles intersect at right angles. The common chord length is 2√(15² - d₁²), where d₁ = 15²/25 = 9. So chord length = 2√(225 - 81) = 2√144 = 2 × 12 = 24 cm.

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