Question 6
An isosceles triangle $ABC$, with $AB=AC$, is inscribed in a circle $\omega$. A point $D$ lies in the interior of segment $BC$, with $BD\ne DC$. Ray $AD$ meets $\omega$ again at $E$. A point $F\ne E$ on $\omega$ satisfies $\angle DFE=90^\circ$. Line $FE$ meets rays $AB,AC$ at $X,Y$, respectively. Prove $\angle XDE=\angle EDY$.
Proposed by Anton Trygub. Source: Evan Chen’s third-party compilation; https://aops.com/community/p27349508. One editorial point; manual grading.
Proposed by Anton Trygub. Source: Evan Chen’s third-party compilation; https://aops.com/community/p27349508. One editorial point; manual grading.