Multiple choice

In a circle of radius 5√13 cm, two parallel chords of 12 cm and 20 cm are lies on the same semi-circle, then find the distance between the two chords?

  1. 2

  2. 3

  3. 2.5

  4. 1.5
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A Correct answer
Explanation

Radius r = 5√13 ≈ 18.03 cm. For 12 cm chord: distance from center d₁ = √((5√13)² - 6²) = √(325 - 36) = √289 = 17 cm. For 20 cm chord: d₂ = √((5√13)² - 10²) = √(325 - 100) = √225 = 15 cm. Distance between chords = d₁ - d₂ = 17 - 15 = 2 cm (assuming they're on same side of center in one semicircle).

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