The triangle \(ABC\) has vertices \(A(7, 7), B (0, 6)\) and \(C (6, 0)\). Write down the equation of the internal bisector of the angle \(BAC\).

Find, by an algebraic method,

- the equation of the circle through the points \(A, B\) and \(C\).
- the equation of the inscribed circle of the triangle \(ABC\), i.e. the circle which touches all three sides of this triangle and which has its centre within the triangle.