Multiple choice

AB and CD are two parallel chords of length 8 cm and 6 cm respectively. If they are 1 cm apart and lie on the same side of the centre of the circle. The radius of the circle is

  1. 3 cm

  2. 6cm

  3. 5cm

  4. 8cm
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let distance from center to chord of length 6 be d1 = sqrt(r^2 - 3^2) = sqrt(r^2 - 9). Distance to chord of length 8 is d2 = sqrt(r^2 - 4^2) = sqrt(r^2 - 16). Given d1 - d2 = 1. sqrt(r^2 - 9) - sqrt(r^2 - 16) = 1. Testing r=5: sqrt(25-9) - sqrt(25-16) = 4 - 3 = 1. Correct.

AI explanation

Using the property that the perpendicular from the centre bisects a chord, the half-lengths of the 8 cm and 6 cm chords are 4 cm and 3 cm respectively. Let the radius be r and the distance from the centre to the 8 cm chord be x, making the distance to the 6 cm chord x plus 1. Applying the Pythagorean theorem gives r squared equals x squared plus 4 squared and r squared equals (x plus 1) squared plus 3 squared. Setting them equal gives x squared plus 16 equals x squared plus 2x plus 1 plus 9, so 2x equals 6 and x equals 3. Substituting x back gives r squared equals 3 squared plus 4 squared, which is 25, so the radius is 5 cm.

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