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The centre of two circle are P and Q ...

The centre of two circle are P and Q they intersect at the points A and B. The straight line parallel to the line segment PQ through the point A intersects the two circles at the point C and D Prove that `CD = 2PQ`

Text Solution

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Let us darw `PM bot CA ` and `QN bot AD`
`therefore AM =(1)/(2)CA and AN = (1)/(2)AD`
`therefore AM + AN = (1)/(2) CA + (1)/(2)AD or , MN = (1)/(2) (CA + AD)`
or `MN = (1)/(2) CD ………… (1)`
Again `CD || PQ and PM bot CD and QN bot CD therefor e PQ = MN`
` therefore PQ = (1)/(2) CD ` [ from (1)] or CD = 2PQ .
`therefore CD = 2PQ `
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