Multiple choice

Two circles of radii 17 cm and 8 cm are concentric. The length of a chord of greater circle which touches the smaller circle is

  1. 15 cm

  2. 16 cm

  3. 30 cm

  4. 34 cm
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The chord of the larger circle tangent to the smaller circle forms a right triangle with the radius of the smaller circle (8) and the radius of the larger circle (17). Half the chord length is sqrt(17^2 - 8^2) = sqrt(289 - 64) = sqrt(225) = 15. The full chord length is 2 * 15 = 30 cm.

AI explanation

Let the chord of the larger circle touch the smaller circle at point P. The radius of the smaller circle is perpendicular to the chord, so it bisects the chord, creating a right triangle with a hypotenuse of 17 centimeters and one leg of 8 centimeters. Using the Pythagorean theorem, half the chord length is the square root of 17 squared minus 8 squared, which is the square root of 289 minus 64, or 15 centimeters. The full length of the chord is 2 multiplied by 15, which equals 30 centimeters.

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