Q. 54.5( 26 Votes )

In figure, AB and CD are common tangents to two circles of unequal radii. Prove that AB = CD


Answer :

Given : AB and CD are two common tangents to two circles of unequal radii.


To Prove : AB = CD



Construction: Produce AB and CD, to intersect at P.


Proof:


Consider the circle with greater radius.


AP = CP [Tangents drawn from an external point to a circle are equal] [1]


Also,


Consider the circle with smaller radius.


BP = BD [Tangents drawn from an external point to a circle are equal] [2]


Substract [2] from [1]. We Get


AP - BP = CP - BD


AB = CD


Hence Proved .


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