Multiple choice

AB and CD are two parallel chords of a circle such that AB = 10 cm and CD = 24 cm, If the chords are on the opposite sides of the centre and the distance between them is 17 cm, the radius of the circle is:

  1. 14 cm

  2. 10 cm

  3. 13 cm

  4. 15 cm
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Draw a perpendicular from the center to the chords. The distances from the center are sqrt(R^2 - 5^2) and sqrt(R^2 - 12^2). Since they are on opposite sides, the sum of these distances is 17. Solving sqrt(R^2 - 25) + sqrt(R^2 - 144) = 17 yields R = 13.

AI explanation

Let the radius be r and the distances from the center to AB and CD be x and y respectively. Since the perpendicular from the center bisects the chord, half of AB is 5 cm and half of CD is 12 cm. Using the Pythagorean theorem gives x squared equals r squared minus 25 and y squared equals r squared minus 144. Since the chords are on opposite sides, x plus y equals 17 cm, which means y equals 17 minus x, so substituting and solving yields x equals 5 cm. Substituting x back into the first equation gives r squared equals 25 plus 25, so r equals 13 cm.

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