Multiple choice

Two concentric circles are of radii 13 cm and 5 cm. The length of the chord of larger circle which touches the smaller circle is

  1. 24 cm

  2. 20 cm

  3. 12 cm

  4. 26 cm
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A Correct answer
Explanation

The radius of the smaller circle (5 cm) is the perpendicular distance from the center to the chord. This forms a right triangle with the radius of the larger circle (13 cm) as the hypotenuse. Half-chord length = sqrt(13^2 - 5^2) = sqrt(169 - 25) = sqrt(144) = 12 cm. Total chord length = 2 * 12 = 24 cm.

AI explanation

The radius of the larger circle forms a right triangle with the radius of the smaller circle and half of the unknown chord. Applying the Pythagorean theorem gives half the chord length as the square root of (13^2 - 5^2), which equals 12 cm. Multiplying by two gives the full chord length of 24 cm.

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