Problem

Source: INMO 2021 Problem 5

Tags: geometry, angles, Equilateral Triangle, equal lengths, INMO, trigonometry



In a convex quadrilateral $ABCD$, $\angle ABD=30^\circ$, $\angle BCA=75^\circ$, $\angle ACD=25^\circ$ and $CD=CB$. Extend $CB$ to meet the circumcircle of triangle $DAC$ at $E$. Prove that $CE=BD$. Proposed by BJ Venkatachala