Asked by HELP HELP HELP MNHS
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...
with solution pls, tnx...
Answers
Answered by
Reiny
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
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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