Q. 45.0( 6 Votes )

In the given figure, common tangents AB and CD to the two circles with centers O1 and O2 intersect at E. Prove that AB = CD.


Answer :

Given: AB and CD are two tangents to two circles which intersects at E .


To Prove: AB = CD


Proof:


As


AE = CE …[1]


[Tangents drawn from an external point to a circle are equal]


And


EB = ED …[2]


[Tangents drawn from an external point to a circle are equal]


Adding [1] and [2]


AE + EB = CE + ED


AB = CD


Hence Proved.


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