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,

  1. the equation of the circle through the points \(A, B\) and \(C\).
  2. 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.