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Two two circle with their centre at P...

Two two circle with their centre at P and Q intersect each other, at the point A and B . Through the point A , a straight line parallel to PQ intersects the two circles at the points C and D respectively . If PQ = 5 cm , then determine the lenght of CD .

Text Solution

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Let `PM bot CD `and `QN bot CD`
`because PQ || CD , therefore PQ = MN`
Now , ` PQ = 5 cm , therefore MN =5 cm`
Also MN = AM + AN
or `MN = (1)/(2) AC + (1)/(2)AD [ because PM bot AC rArr AM = (1)/(2) AC and QN bot AD rArr AN = (1)/(2) AD.] or MN = (1)/(2) (AC + AD)`
or ` 5 = (1)/(2) xx CD[because AC + AD = CD] or CD = 5 xx 2 =10`
`therefore` lenght of hte chord CD = 10 .
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