# 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 $\angle DEF$?

×