Multiple choice

In a circle with center O and radius 5 cm, AB and CD are two parallel chords of lengths 6 cm and x cm, respectively and the chords are on the opposite side of the center O. The distance between the chords is 7 cm. What is the value of x?

  1. 9

  2. 8

  3. 12

  4. 10
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

For chord AB (length 6): perpendicular distance from center d₁ = √(5²-3²)=4. For chord CD (length x): distance d₂ = √(25-(x/2)²). Since chords are opposite sides, d₁ + d₂ = 7, so 4 + √(25-(x/2)²)=7, giving √(25-(x/2)²)=3, so 25-(x/2)²=9, (x/2)²=16, x/2=4, x=8.

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