11 The points \(A ( - 1,6 ) , B ( 1,0 )\) and \(C ( 13,4 )\) 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 .