Multiple choice

Two equal circles of radius 4 cm intersect each other such that each passes through the centre of the other. The length of the common chord is :

  1. $2\sqrt{3} cm$
  2. $3\sqrt{3} cm$
  3. $4\sqrt{3} cm$
  4. $\sqrt{3} cm$
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C Correct answer
Explanation

When two circles of equal radius intersect such that each passes through the other's center, their centers are 4 cm apart. The common chord is perpendicular to the line joining centers. Each center is 2 cm from the chord (half the distance). Using right triangle: chord/2 = √(4² - 2²) = √12 = 2√3. Full chord = 4√3 cm.

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