Multiple choice

Find the distance of a perpendicular from the centre of a circle to the chord if the diameter of the circle is 30 cm and its chord is 24 cm.

  1. $6 cm$
  2. $7 cm$
  3. $9 cm$
  4. $10 cm$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Diameter = 30, radius = 15. Chord = 24, half-chord = 12. Distance = sqrt(15^2 - 12^2) = sqrt(225 - 144) = sqrt(81) = 9 cm.

AI explanation

Using the perpendicular from the center to a chord formula, half the chord length squared plus the perpendicular distance squared equals the radius squared. The radius is 15 cm and half the chord is 12 cm, giving the equation 12 squared plus d squared equals 15 squared. Solving 144 plus d squared equals 225 yields d squared equals 81, so the distance is 9 cm.

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