The points $A(-2, 3)$, $B(3, 0)$ and $C(6, 5)$ are positioned on the circumference of a circle whose centre is $D$.
(a)[2]
Show that $\angle ABC = 90^\circ$.
(b)[1]
Therefore, state the coordinates of $D$.
(c)[2]
Find the equation of the circle.
(d)[5]
Point $E$ is on the circle’s circumference and $BE$ is a diameter. Find an equation for the tangent to the circle at $E$.
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