Multiple choice

The length of the common chord of two intersecting circles is 24 cm. If the diameters of the circles are 30 cm. and 26 cm., then the distance between the centres in cm. is -

  1. 13

  2. 14

  3. 25

  4. 16
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

For intersecting circles with common chord length L and radii r1 and r2, the distance between centers d = sqrt(r1^2 - (L/2)^2) + sqrt(r2^2 - (L/2)^2). Here r1=15, r2=13, L=24. So d = sqrt(225-144) + sqrt(169-144) = sqrt(81) + sqrt(25) = 9 + 5 = 14 cm.

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