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math

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Two equal circles of radius 8cm intersect at X and Y. If the line joining the centers is 12cm long, find the length of XY.

with solution pls, tnx...

  • math -

    let the length of the overlap be x
    then 8+8-x=12
    x=4
    So now you can construct a right-angled triangle by joining one of the centres to X
    Its hypotenue will be 8
    and its base will be 8 - (1/2)of4 = 6 and its height is 1/2 of XY, call it h
    h^2 + 6^2 = 8^2
    h^2 = 64-36 = 28
    h = √28 = 2√7

    So XY = 4√7

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