5.2.4.23 Various problems on the plane

In a triangle \( A B C \) with sides \( A B=8 \) and \( A C=5 \) the altitude \( A D \) is drawn. Find the area of ​​a circle circumscribed about a triangle if it is known that one of the distances from the point \(D\) to the ends of the side \(B C\) is twice the other.