Problem

A circle has equation $x^2+y^2+4y-21=0$ and a straight line has equation $2x+y-8=0$. The line intersects the circle at two points.

(a) Find the coordinates of these two points of intersection.

(b) The circle has centre $C$ and the two points of intersection are denoted by $A$ and $B$.

Find the area of the triangle $ABC$.