Multiple choice

Two parallel chords AB and CD of a circle are of lengths 60 cm and 80 cm respectively. They are on the same side of the centre O and 10 cm apart. What is the diameter of the circle?

  1. 120 cm

  2. 110 cm

  3. 100 cm

  4. 90 cm
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C Correct answer
Explanation

Using the properties of chords and the Pythagorean theorem, let r be the radius. The distances from the center to the chords are d1 and d2. We have r^2 = 30^2 + d1^2 and r^2 = 40^2 + d2^2. Given d2 - d1 = 10, solving the system yields r = 50. The diameter is 2r = 100 cm.

AI explanation

A perpendicular from the center to a chord bisects it, giving half-lengths of 30 cm for AB and 40 cm for CD. Using the Pythagorean theorem, the distance from the center to AB is the square root of r squared minus 30 squared, and the distance to CD is the square root of r squared minus 40 squared. Since the chords are 10 cm apart on the same side, the difference of these distances is 10, leading to the equation square root of r squared minus 900 minus the square root of r squared minus 1600 equals 10. Solving this gives a radius of 50 cm, so the diameter is 100 cm.

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