$20 \cdot 37$ Given a right triangle $\triangle ABC$ with a right angle at $B$, a circle is drawn with the diameter $BC$ intersecting the hypotenuse $AB$ at $D$. A tangent line through $D$ intersects $CA$ at $F$. These conditions are insufficient to prove:
(A) $DF$ bisects $CA$.
(B) $DF$ bisects $\angle CDA$.
(C) $DF=FA$.
(D) $\angle A=\angle BCD$.
(E) $\angle CFD=2\angle A$.