Question 51
Let $ABC$ be a triangle such that $AB = 6$, $BC = 5$, $AC = 7$. Let the tangents to the circumcircle of $ABC$ at $B$ and $C$ meet at $X$. Let $Z$ be a point on the circumcircle of $ABC$. Let $Y$ be the foot of the perpendicular from $X$ to $CZ$. Let $K$ be the intersection of the circumcircle of $BCY$ with line $AB$. Given that $Y$ is on the interior of segment $CZ$ and $YZ = 3 \, CY$, compute $AK$.
Proposed by: Allen Liu
Proposed by: Allen Liu