11. Find the vertex and calculate the required area

A point \(A\) is equidistant from the points \(B (13, 14)\) and \(C (1, 4)\). If one of the vertices of the triangle is twice the point \(A\), then find the area of the triangle made by the points \(B\) and \(C\) with this vertex.

 

Answer:

 

The area of the required triangle is  square units.