Constructions Around a Circle

Geometry Level 5

Outside of circle Γ \Gamma, point AA is chosen. Tangents ABAB and ACAC to Γ\Gamma are drawn, with B,CB, C on the circumference of Γ\Gamma. On the extension of ABAB, DD is a point such that BB is between AA and DD, and ADC=25 \angle ADC = 25 ^ \circ. The circumcircle of ADCADC intersects Γ\Gamma again at EE (different from point CC ). FF is the foot of the perpendicular from BB to DCDC. What is the measure (in degrees) of DEF\angle DEF?

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