Q10 of 47 Page 1

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


Given: Two circles with centre’s O and O’. AB and CD are common tangents on both circles


Construction: Produce the tangents AB and CD so as they intersect at point P



To Prove: AB = CD


Proof:


AP = PC …(1)


(length of tangents drawn from an external point to the circle are equal)


Similarly,


PB = PD … (2)


(length of tangents drawn from an external point to the circle are equal)


Adding (1) and (2), we get


AP + PB = PC + PD


⇒ AB = CD


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