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Let AC and EC are two secants intersect circle at B and D respectively . It mean A,B,D and E lies on circumference of the circle and C is an external point.

By secant and tangent theorem ,

AC x BC =EC x CD

But

AE =AB+BC

Given AB=8 ,BC=6 ,EC=12 and DC=y (say)

AE=8+6

=14

Thus

14 x 6= 12 x y

y=(14 x6)/12

=7

Thus DC=7

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