Multiple choice

The length of the common chord of two circles of radii 30 cm and 40 cm whose centers are 50 cm apart, is (in cm)-

  1. 48

  2. 26

  3. 24

  4. 16
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A Correct answer
Explanation

For two circles with radii 30 and 40 cm and center distance 50 cm, note that 30² + 40² = 50², so the circles intersect at right angles. The common chord length = 2 × (product of radii / center distance) = 2 × (30 × 40)/50 = 48 cm. This can also be derived using perpendicular distance from centers to the chord.

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