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Two circles with centres O and O' inters...

Two circles with centres O and O' intersect at two points A and B. A line PQ is drawn parallel to OO' through A (or B) intersecting the circles at P and Q. Prove that PQ=200'.

Text Solution

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Draw `Oabotl` and `O'Bbotl`
Now, `OA bot l`
`rArrOAbtoCP`
`rArrCA=AP` (perpendicular form centre bisects the chord)
`CP=2CA=2AP` ......(1)
and `O'Bbotl`
`rArrO'BbotDP`
`BD=BP`
`PD=2DB=2PB` ........(2)
`therefore CD =CP+PD`
`rArrCD=2AP+2PB`
[using (1) and (2) ]
`rArrCD=2(AP+PB)`
`=2AB=2OO`.
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