6 The points \(\mathrm { A } ( - 1,6 ) , \mathrm { B } ( 1,0 )\) and \(\mathrm { C } ( 13,4 )\) are joined by straight lines.
- Prove that the lines AB and BC are perpendicular.
- Find the area of triangle ABC .
- A circle passes through the points A , B and C . Justify the statement that AC is a diameter of this circle. Find the equation of this circle.
- Find the coordinates of the point on this circle that is furthest from B.