Multiple choice

The radius of a circle is $2.5$ $cm .$ $AB$ and $CD$ are two parallel chords $2.7$ $cm$ apart. If $A B = 4.8 \mathrm { cm }$ .then $\mathrm { CD }$ is equal to

  1. $4.8$ $cm$
  2. $2.4$ $cm$
  3. $3$ $cm$
  4. $4$ $cm$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let the center be O. Distance to AB is 2.7. Half of AB is 2.4. Radius is 2.5. Distance from center to AB is sqrt(2.5^2 - 2.4^2) = 0.7. Since chords are parallel and 2.7 apart, the distance from center to CD is 2.7 - 0.7 = 2.0. Half of CD = sqrt(2.5^2 - 2.0^2) = 1.5. CD = 3.0 cm.

AI explanation

The distance from center O to chord AB is found using the perpendicular distance formula: sqrt(2.5^2 - (4.8/2)^2) = sqrt(6.25 - 5.76) = sqrt(0.49) = 0.7 cm. Since the total distance between the parallel chords is 2.7 cm, the distance from center O to chord CD is 2.7 - 0.7 = 2.0 cm. Using the chord length formula again, the length of CD is 2 * sqrt(2.5^2 - 2.0^2) = 2 * sqrt(6.25 - 4.00) = 2 * sqrt(2.25) = 2 * 1.5 = 3 cm.

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