If in a two triangles corresponding angles are equal then their corresponding sides are in same ratio hence two triangle are similar
Shaalaa.com | Similar Triangles Theorem
O is any point in the interior of ΔABC. Bisectors of ∠AOB, ∠BOC and ∠AOC intersect side AB, side BC, side AC in
F, D and E respectively.
BF × AE × CD = AF × CE × BD