Question

In the adjoining figure, prove that AD+BC = AB+CD​

Answer 1

Answer:

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Step-by-step explanation:

so here pd and qd are tangent segments drawn from external point d.

ap and as are tangent segments drawn from external point a

bs and br are tangent segments drawn from external point b and also qc and rc are tangent segments drawn from external point c to the adjoining circle

thus since tangent segments drawn from external point are equal in length

pd=qd (1)

ap=as (2)

br=bs (3)

rc=qc (4)

adding all the equations

we obtain

(pd+ap)+(br+rc)=(qd+as)+(bs+qc)

so ad+bc=(qd+qc)+(as+bs) due to colinearity of points

so ie ad+bc=dc+ab

ie AD+BC=AB+CD

thus proved