Multiple choice

Two chords $AB$ and $CD$ of lengths $5\ cm$ and $11\ cm$ respectively of a circle are parallel to each other and are on opposite sides of its centre. If the distance between $AB$ and $CD$ is $6\ cm$, find the radius of the circle.

  1. $\dfrac{5\sqrt{5}}{2}$
  2. $\dfrac{11\sqrt{5}}{2}$
  3. $\dfrac{5\sqrt{5}}{3}$
  4. $\dfrac{5\sqrt{3}}{2}$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let the radius be r. Distance from center to chord AB (length 5) is d1 = sqrt(r^2 - 2.5^2). Distance to chord CD (length 11) is d2 = sqrt(r^2 - 5.5^2). Since they are on opposite sides, d1 + d2 = 6. Solving sqrt(r^2 - 6.25) + sqrt(r^2 - 30.25) = 6 leads to r = sqrt(125/4) = 5*sqrt(5)/2.

AI explanation

Let the radius be r, and let the distances from the center to the 5 cm and 11 cm chords be x and y. Using the chord-length formula where half the chord squared plus the distance squared equals the radius squared, we get x squared plus 2.5 squared equals r squared and y squared plus 5.5 squared equals r squared. Since the chords are on opposite sides and 6 cm apart, x plus y equals 6. Solving the system of equations yields the radius as 5 root 5 divided by 2 cm.

Keep practicing — related questions