INTEGER TYPE -2

Three points P(a,b) ,Q(c,d) and R(e,f) satisfy the inequality $x^2$ + $y^2$ -6x-8y < 0 such that 'P' lies at a least distance from A(-2,4) and Q and R lies at maximum distance from A , where a,b,c,d,e and f are integers. The internal bisector of P of triangle PQR intersects the tangent at origin and the point ( $\frac{c+e}{2}$ +1,d) to the circle $x^2$ + $y^2$ -6x-8y=0 . If the area of Triangle formed by these three lines is T , then $\frac{3T}{50}$ is equal to ?