Question 92
The triangle $ABC$ has circumcircle $\Gamma$ with centre $O$, $AO \cap BC = \{X\}$, $AO \cap \Gamma = \{Y\}$, and $\frac{AX}{XY} = k$, $k \gt 1$. The tangent to $\Gamma$ at $Y$ meets $AB$ and $AC$ in $M$, respectively $N$. Find $k$ so that the quadrilateral $OMNC$ is cyclic.
Mihaela Berindeanu
Mihaela Berindeanu