Multiple choice

A chord of length 12cm is at a distance of 3cm from the centre of a circle. then its radius is

  1. $2\sqrt { 5 } $cm
  2. $3\sqrt { 5 } $cm
  3. $4\sqrt { 5 } $cm
  4. $6\sqrt { 5 } $cm
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B Correct answer
Explanation

A perpendicular from the center to a chord bisects the chord. This creates a right triangle with legs of 6 cm (half the chord) and 3 cm (distance from center). The radius is the hypotenuse: sqrt(6^2 + 3^2) = sqrt(36 + 9) = sqrt(45) = 3*sqrt(5).

AI explanation

The perpendicular from the centre to the chord bisects the chord, so the half-length is 6 cm. Using the Pythagorean theorem in the right triangle formed by the radius, half-chord and the distance, we get r squared equals 6 squared plus 3 squared. This gives r squared equals 45, so the radius is the square root of 45, which simplifies to 3 root 5 cm.

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