A circle has equation $(x-a)^2+(y-3)^2=20$. The straight line $y=\frac{1}{2}x+6$ is tangent to the circle at point $P$.
(a)[5]
Demonstrate that one possible value of $a$ is $4$ and determine the remaining possible value.
(b)[4]
When $a=4$, determine the equation of the normal to the circle at $P$.
(c)[4]
When $a=4$, determine the equations of the two tangents to the circle that are parallel to the normal found in (b).
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