A circle contains triangle ABC. For each side, construct the perpendicular bisector and extend it to the exterior of the triangle to the circle. The three such lengths are 1, 2, 3, as shown.

Point P is in the interior of triangle ABC, and the lines through P are parallel to the sides of ABC.
The three triangles shown in the diagram have areas of 4, 9, and 49.
What is the area of triangle ABC?