Multiple choice

If radii of two concentric circles are 4 cm and 5 cm, then the length of each chord of one circle which is tangent to the other circle is

  1. 3 cm

  2. 6 cm

  3. 9 cm

  4. 1 cm
Reveal answer Fill a bubble to check yourself
B 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 (4 cm) and the radius of the larger circle (5 cm). By the Pythagorean theorem, half the chord length is sqrt(5^2 - 4^2) = sqrt(25 - 16) = sqrt(9) = 3 cm. The full chord length is 2 * 3 = 6 cm.

AI explanation

The chord of the larger circle acts as a tangent to the smaller circle, so the radius of the smaller circle forms a right angle with this chord at its point of contact. This creates a right triangle with the larger circle's radius of 5 cm as the hypotenuse and the smaller circle's radius of 4 cm as one leg. Applying the Pythagorean theorem, the half-length of the chord is the square root of (25 minus 16), which equals 3 cm, making the full length of the chord 6 cm.

Keep practicing — related questions