The inscribed circle O of the right triangle ABC, the hypotenuse AB at point D, the tangent BC at point F, and the intersection AC of the extension line of Bo at point E

The inscribed circle O of the right triangle ABC, the hypotenuse AB at point D, the tangent BC at point F, and the intersection AC of the extension line of Bo at point E

I'll just tell you the method, and then you can do it yourself
1) After transforming multiplication into proportional form, you may know how to do it. After transformation, you need to think of finding out the similarity between the two triangles concerned. After doing so, you will find that there is no BD term, but there is BF term. Therefore, you need to prove BD = BF. In this step, you need to use right triangle congruence
Hope you understand!