A problem by Fahim Shahriar Shakkhor

Level pending

In \(ABC\) equilateral triangle the length of each side is \(24\). \(D\) is the midpoint of \(BC\). \(DE\) and \(DF\) are drawn perpendicular to \(AB\) and \(AC\) respectively from the point \(D\). \(O\) is the intersection point of \(AD\) and \(EF\). Find the circum-radius of \(\triangle AOF\).

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