A geometry problem by Rudresh Tomar

Geometry Level 3

In the figure above, two brown lines are perpendicular to each other and they intersect at the point \(G\).

Two circles are drawn such that they are tangential to these two lines at \(F,H,E\) and \(D\).

If \(\overline{BC} = \sqrt{50} \), find \(\overline{AB} \times \overline{AC} \).

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