On a circle, points A, B, C, D lie counterclockwise in this order. Let the orthocenters of A B C, B C D, C D A, D A B be H, I, J, K respectively. Let H I=2, I J=3, J K=4, K H=5. Find the value of 13(B D)^{2}.
On a circle, points A, B, C, D lie counterclockwise in this order. Let the orthocenters of A B C, B C D, C D A, D A B be H, I, J, K respectively. Let H I=2, I J=3, J K=4, K H=5. Find the value of 13(B D)^{2}.