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In the adjoining figure, common tangents...

In the adjoining figure, common tangents AB and CD to two circles intersect at P.
Prove that AB=CD.

Text Solution

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Since PA and PC are two tangents to a circle with centre O from an external point P.
`:." "PA=PC" "…(1)`
Also, since PB and PD are two tengents to a circle with centre O' from an external point P.
Circles
`:." "PB=PD`
Adding (2) and (1), we get
`PA+PB=PC+PD`
`rArr" " AB = CD" "` (`because` AB and CD are two straight lines) Hence Proved.
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