I have a doubt in approaching this math problem

Given $P,Q$ are two points on the curve $y=log_\dfrac{1}{2}(x-0.5)+log_2\sqrt{4x^2-4x+1}$ , $P$ is also lying on the circle $x^2+y^2=10$ . If $Q$ lies inside the given circle such that it's abscissa is integer then $\vec{OP}.\vec{OQ}$ is equal to :- $(a)4$ $(b)8$ $(c)2$ $(d)10$

Pls post the solution in DETAIL....

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I have a doubt in approaching this math problem

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