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If common tangent to parabola y^2=4x and...

If common tangent to parabola `y^2=4x` and `x^2=4y` also touches the circle `x^2+y^2=c^2`, then find the value of C.

A

`(1)/(2 sqrt2)`

B

`(1)/(sqrt2)`

C

`(1)/(4)`

D

`(1)/(2)`

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