Question

in fig, common tangents AB and CD to the two circles with centers O1 & O2 intersect at E. prove that ab=cd.
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Answer 1

join OA and OC

join OD and ob

By RHS axiom,

AO1E=~CO1E

and DOE=~BOE

By CPCT,

AE=CE & DE=BD

Then, AE+BE=DE+CE

AB =CD

Hence proved

Answer 2

hey mate here is ur answer✌️✌️
Tangent from a common point to the circle are equal to each other.
BE=DE. ( tangent from a common point E to the circle )......1
AE= CE (tangent from a common point E.).....2
add equation 1 and 2 .
AE+BE=DE+CE
AB=CD.
HENCE PROVED ...
HOPE IT HELPS UHHHH.....