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Question

In figure, AB and CD are common tangents to two circles of unequal radii. Prove that AB=CD.
1603132_3104f94696a34ef8b031bf856461940f.png

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Solution

Given : Circles C1 and C2 of radii r1 and r2 respectively and r1<r2.


AB and CD are two common tangents.


To prove : AB=CD


Construction : Produce AB and CD upto P where both tangents meet.


Proof : Tangents from an external point to a circle are equal.


For circle C1,PB=PD __(i)


and the circle C2,PA=PC __(ii)


Subtracting (i) from (ii), we have


PAPB=PCPD


AB=CD


Hence, proved.


1795713_1603132_ans_9219878cb88d47619ad8a39e45492ee8.png

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