PP' and QQ' are two direct common tangen...

PP' and QQ' are two direct common tangents at two circles intersecing in point A and B.The common chord produced intersects PP' in R and QQ' in S. prove that `RS^2=PP'^2+AB^2`

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Power of circle
`RP^2=RA*RB`
`RP'^2=RA*RB`
`RP^2=RP'^2`
`RP=RP'`
`PP'=RP+RP'`
`RP=RP'=1/2PP'`
`RS^2-AB^2=(RS+AB)(RS-AB)`
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