Problem

Problem of the Day #64

Consider a line segment $AC$ with a point $B$ between $A$ and $C$ such that $AB = 12$ . Circle $\gamma$ is drawn with diameter $AB$ , and the tangent from point $C$ to $\gamma$ is tangent at a point $X$ . Let $Y$ denote the foot of the perpendicular from $B$ to $XC$ . Find the maximum possible value of $AY$ .

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Category: Problem of the Day
Points: 4
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