Multiple choice

Two parallel chords are on one side of the centre of a circle. The length of the two chords is 24 cm and 32 cm. If the distance between the two chords is 8 cm, then what is the area (in cm2) of the circle?

  1. 724.14

  2. 832.86

  3. 924.12

  4. 988.32
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let the radius be r and distance from center to chords be x and x+8. Using Pythagoras: r^2 = x^2 + 16^2 and r^2 = (x+8)^2 + 12^2. x^2 + 256 = x^2 + 16x + 64 + 144. 16x = 48 => x = 3. r^2 = 3^2 + 16^2 = 9 + 256 = 265. Area = pi * r^2 = 3.14159 * 265 = 832.52. Option B is the closest.

AI explanation

Using the perpendicular bisector property, the distance from the center to the 32 cm chord is the square root of (r squared minus 16 squared), and the distance to the 24 cm chord is the square root of (r squared minus 12 squared). The distance between the chords is 8 cm, so the square root of (r squared minus 256) minus the square root of (r squared minus 144) equals 8. Solving this equation gives a radius of approximately 16.28 cm, and the area of the circle is pi multiplied by r squared, which is 3.14 multiplied by 16.28 squared to give 832.86 square cm.

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