2017 JBMO Problems/Problem 3


Let $ABC$ be an acute triangle such that $AB\neq AC$ ,with circumcircle $\Gamma$ and circumcenter $O$. Let $M$ be the midpoint of $BC$ and $D$ be a point on $\Gamma$ such that $AD \perp  BC$. let $T$ be a point such that $BDCT$ is a parallelogram and $Q$ a point on the same side of $BC$ as $A$ such that $\angle{BQM}=\angle{BCA}$ and $\angle{CQM}=\angle{CBA}$. Let the line $AO$ intersect $\Gamma$ at $E$ $(E\neq A)$ and let the circumcircle of $\triangle ETQ$ intersect $\Gamma$ at point $X\neq E$. Prove that the point $A,M$ and $X$ are collinear .


See also

2017 JBMO (ProblemsResources)
Preceded by
Problem 2
Followed by
Problem 4
1 2 3 4
All JBMO Problems and Solutions