SOLUTION: Two circles with centres X and Y intersect at A and B if the radii of the circles are 20cm and 15cm and if AB=24cm, find the distance between the centres.

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Question 1161529: Two circles with centres X and Y intersect at A and B if the radii of the circles are 20cm and 15cm and if AB=24cm, find the distance between the centres.
Answer by ikleyn(52788) About Me  (Show Source):
You can put this solution on YOUR website!
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(1)  Connect the centers X and Y by the segment XY.

     Let C be the intersection point of segments XY and AB.

     Notice that AC = BC = half of AB = 24/2 = 12 cm



(2)  Then XAC is the right triangle.

     Its leg XC is  sqrt%2820%5E2-12%5E2%29 = sqrt%28400-144%29 = sqrt%28256%29 = 16 cm.



(3)  Similarly, YAC is the right triangle.

     Its leg YC is  sqrt%2815%5E2-12%5E2%29 = sqrt%28225-144%29 = sqrt%2881%29 = 9 cm.



(4)  Now the length of the segment  XY  is 16+9 = 25 cm.    



ANSWER.  The distance between the centers is 25 cm.


Solved.