Question 40
Problem 1 (7 points). Let $(O)$ be a circle and $B,C$ fixed points on it such that $BC$ is not a diameter. Point $A$ varies on $(O)$, with $A\ne B,C$. Let $D,K,J$ be the midpoints of $BC,CA,AB$, respectively; let $E,M,N$ be the perpendicular projections of $A,B,C$ onto $BC,DJ,DK$, respectively. The tangents at $M,N$ to the circumcircle of $EMN$ meet at $T$. Prove that $T$ is fixed.
