Two chords PQ and MN of length 11 cm and 5 cm respectively of a circle are parallel to each other and are one the opposite sides of its centre. If the distance between chord MN and chord PQ is 6 cm find the radius of the circle
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$\displaystyle \frac{10 \sqrt{5}}{2} cm$
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$\displaystyle \frac{5 \sqrt{5}}{4} cm$
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$\displaystyle \frac{5 \sqrt{5}}{2} cm$
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$\displaystyle \frac{5 \sqrt{10}}{2} cm$
C
Correct answer
Explanation
Let r be the radius. Distance from center to chord PQ (length 11) is sqrt(r^2 - 5.5^2). Distance to chord MN (length 5) is sqrt(r^2 - 2.5^2). Since they are on opposite sides, the sum of distances is 6. Solving sqrt(r^2 - 30.25) + sqrt(r^2 - 6.25) = 6 leads to r = 5*sqrt(5)/2.