{"status": "success", "data": {"description_md": "Consider a circle $\\omega$ with center $O$. Let $AB$ be a chord of $\\omega$, not passing through $O$. Let the tangents to $\\omega$ at $A$, $B$ intersect at $P$. Let $C$ be on the minor arc $AB$ with $AC > BC > 0$, and let $PC$ intersect $\\omega$ at $D \\neq C$. Define $Q_1,Q_2$ to be the intersections of $(COD)$ and line segment $AB$ (with $Q_1 = Q_2$ if there is only $1$ intersection), and $R = CD \\cap AB$. If $PC = 12$, $PD = 20$, and $Q_1R = Q_2R = 5$, find the sum of all possible values of $r^2$ ($r$ is the radius of $\\omega$).", "description_html": "

Consider a circle \\omega with center O. Let AB be a chord of \\omega, not passing through O. Let the tangents to \\omega at A, B intersect at P. Let C be on the minor arc AB with AC > BC > 0, and let PC intersect \\omega at D \\neq C. Define Q_1,Q_2 to be the intersections of (COD) and line segment AB (with Q_1 = Q_2 if there is only 1 intersection), and R = CD \\cap AB. If PC = 12, PD = 20, and Q_1R = Q_2R = 5, find the sum of all possible values of r^2 (r is the radius of \\omega).

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