Multiple choice

The radius of a circle is 10 cm. There are two chords of 12 cm and 16 cm on either side of the center. Find the distance between the two parallel chords.

  1. 14

  2. 16

  3. 15

  4. 20

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A Correct answer
Explanation

For a chord of length L in a circle of radius R, the perpendicular distance from center to chord is d = √(R² - (L/2)²). For the 12 cm chord: d₁ = √(100 - 36) = 8 cm. For the 16 cm chord: d₂ = √(100 - 64) = 6 cm. Since chords are on opposite sides of the center, total distance = 8 + 6 = 14 cm. Option B (16 cm) and C (15 cm) don't account for both distances correctly. Option D (20 cm) exceeds the diameter (20 cm), which is impossible.