Multiple choice

Two parallel chords in a circle have lengths 6 cm and 8 cm respectively. The distance between them is 1 cm. Then, the diameter of the circle is

  1. 12 cm

  2. 14 cm

  3. 10 cm

  4. 9 cm

  5. 8 cm
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let r be the radius. The distances from the center to the chords are d1 = sqrt(r^2 - 3^2) and d2 = sqrt(r^2 - 4^2). Given d2 - d1 = 1, solving sqrt(r^2 - 9) - sqrt(r^2 - 16) = 1 leads to r = 5. Diameter = 2r = 10 cm.

AI explanation

Using the property of perpendicular bisectors, the distance from the center to the 6 cm chord is the square root of (r squared minus 3 squared) and the distance to the 8 cm chord is the square root of (r squared minus 4 squared). Since the 1 cm distance between the chords forces them to be on the same side of the center, the difference of these distances is 1 cm, leading to the equation square root of (r squared minus 9) minus square root of (r squared minus 16) equals 1. Solving this equation gives a radius of 5 cm. The diameter is twice the radius, which is 10 cm.

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