Multiple choice

In a circle with centre O, AB and CD are two parallel chords on the same side of the diameter. If AB = 12 cm, CD = 18 cm and distance between the chords AB and CD is 3 cm, then find the radius of the circle (in cm).

  1. 15

  2. 9

  3. 12

  4. 3√13
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D Correct answer
Explanation

Let distance from center to AB = d₁, to CD = d₂. d₁ = √(r² - 6²) = √(r² - 36), d₂ = √(r² - 9²) = √(r² - 81). Since chords are parallel and 3 cm apart: d₂ - d₁ = 3. √(r² - 81) - √(r² - 36) = 3. Solving: r² = 117, r = √117 = 3√13.

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