Constructions Around a Circle

Geometry Level 5

Outside of circle $\Gamma$ , point $A$ is chosen. Tangents $AB$ and $AC$ to $\Gamma$ are drawn, with $B, C$ on the circumference of $\Gamma$ . On the extension of $AB$ , $D$ is a point such that $B$ is between $A$ and $D$ , and $\angle ADC = 25 ^ \circ$ . The circumcircle of $ADC$ intersects $\Gamma$ again at $E$ (different from point $C$ ). $F$ is the foot of the perpendicular from $B$ to $DC$ . What is the measure (in degrees) of $\angle DEF$ ?