Multiple choice

AB and CD are two parallel chords of a circle such that AB = 5 cm and CD = 11 cm. If distance between them is 3 cm then radius of the circle is

  1. $\displaystyle 2\sqrt{146} cm$
  2. $\displaystyle \sqrt{146} cm$
  3. $\displaystyle \frac{\sqrt{146}}{2} cm$

  4. None of these
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let the center be O and radius be r. Distance from center to chord AB is d1, to CD is d2. d1^2 + (5/2)^2 = r^2 and d2^2 + (11/2)^2 = r^2. Given d1 - d2 = 3 (or d1 + d2 = 3 if center is between chords). Assuming center is between, d1+d2=3. Solving the system yields r = sqrt(146)/2.

AI explanation

Let the radius of the circle be r. The perpendicular distance from the center to the 5 cm chord is sqrt(r^2 - (2.5)^2) and the distance to the 11 cm chord is sqrt(r^2 - (5.5)^2). Assuming the chords are on the same side of the center, the distance between them is 3 cm, giving the equation sqrt(r^2 - 6.25) - sqrt(r^2 - 30.25) = 3. Solving this equation yields r = sqrt(146)/2. The result is r = sqrt(146)/2 cm.

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