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 $\angle DEF$ ?

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Constructions Around a Circle

Excel in math and science

Master concepts by solving fun, challenging problems.

It's hard to learn from lectures and videos

Learn more effectively through short, interactive explorations.

Used and loved by over 7 million people

Learn from a vibrant community of students and enthusiasts, including olympiad champions, researchers, and professionals.

Learn from a vibrant community of students and enthusiasts,
including olympiad champions, researchers, and professionals.

Learn from a vibrant community of students and enthusiasts,
including olympiad champions, researchers, and professionals.