The centre of a circle is at $B\,(5, 1)$, and $A\,(-1, -2)$ lies on the circle.
(a)[3]
Find the equation for the circle.
(b)[4]
Point $C$ is positioned so that $AC$ is a diameter of the circle. Point $D$ has coordinates $(5, 16)$. Show that $DC$ is a tangent to the circle.
(c)[2]
The second tangent from $D$ to the circle meets the circle at $E$. Find the coordinates of $E$.
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