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Two circles of unequal radii neither tou...

Two circles of unequal radii neither touch nor intersect each other. Whether the common tangents AB and CD are always equal? If no, then give explanation of it and if your answer is yes, then prove it.

Text Solution

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Let the two tangents AB and CD on producing meet at P.
Since PA and PC are tangents from an external point P to the circle with centre O
`:." "PA=PC" "…(1)`

Also, PB and PD are tangents from an external point P to the circle with ecntre O'.
`:." "PB=PD" "...(2)`
Subtracting (2) from (1), we get
`PA-PB=PC-PD`
`implies" "AB=CD` Hence Proved.
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