Problem

The diagram shows the circle with equation $x^2 + y^2 - 14x + 8y + 36 = 0$ and the line $y = -2$. The line intersects the circle at the points $A$ and $B$. The centre of the circle is $C$.

(a) Find the coordinates of $A$, $B$ and $C$.

(b) Find the angle $ACB$ in radians. Give your answer correct to 3 significant figures.

(c) The chord $AB$ divides the circle into two segments.

Find the area of the larger segment.