Multiple choice

Directions : Select the correct alternative from the given choices. Find the distance (in cm) between two parallel chords, drawn one on each side of the center of a circle of radius 65 cm, if their lengths are 104 cm and 120 cm respectively.

  1. 14

  2. 30

  3. 60

  4. 64
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D Correct answer
Explanation

Distance from center to chord of length 104 is sqrt(65^2 - 52^2) = sqrt(4225 - 2704) = sqrt(1521) = 39. Distance from center to chord of length 120 is sqrt(65^2 - 60^2) = sqrt(4225 - 3600) = sqrt(625) = 25. Since they are on opposite sides, the distance between them is 39 + 25 = 64.

AI explanation

A perpendicular from the center to a chord bisects the chord, creating two right triangles with a hypotenuse of 65 cm. For the first chord, the distance is the square root of (65 squared minus 52 squared), which is 39 cm. For the second chord, the distance is the square root of (65 squared minus 60 squared), which is 25 cm. Adding these distances because the chords are on opposite sides of the center gives a total distance of 64 cm.

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