This problem cannot be proved. . I'll write it out in words and you draw it yourself. If the point M is tangent to AC so that CM=BF, then the triangles BEF and CEM are congruent triangles, so EF=EM. . . Because BF=CD and CD=CM. If you want to prove EF=ED, prove ED=EM. . . If ED=EM, CD=CM and CE=CE, then the triangle CEM and CDM are congruent, then the angle ECM= the angle ECD=90 degrees. But this is not true because the angle ECM= the angle FBE.

Hope to adopt. . Thank you. You can keep asking me if you don't understand. . .