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Two circles whose centres are O and O...

Two circles whose centres are `O` and `O '` intersect at `Pdot` Through `P ,` a line `l` parallel to `O O '` intersecting the circles at `C\ a n d\ D` is drawn. Prove that `C D=2\ O O '`

Text Solution

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Draw `OA _|_ l` and `O'B_|_ l`
`OA _|_l`
`implies OA _|_ CP `
`implies CA = AP`
`implies CP =2AP` …..(i)
Again, `O'B _|_l`
`implies O' B_|_PD`
`implies PB =BD`
`implies PD =2PB` ….(ii)
`:. CD=CP +PD =2(AP +PB) =2AB =2OQ'` [from (i) and (ii)]
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