Segments at equal angles from the opposite sides of a cyclic quadrilateral | geometry | intermediate

Episode 73.

Segments at equal angles from the opposite sides of a cyclic quadrilateral | geometry | intermediate.
The cyclic quadrilateral formed by segments at equal angles from the opposite sides of another cyclic quadrilateral | plane geometry | intermediate level.

Branch of mathematics: plane geometry.
Difficulty level: intermediate.

Theorem. Let $ABCD$ be a cyclic quadrilateral. let $E$ and $F$ be points on the side $AD$ such that $\angle{ABE}=\angle{DCF}$. Then the quadrilateral $BCFE$ is cyclic.

Mathematics. Geometry. Plane geometry.
#Mathematics #Geometry #PlaneGeometry

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