In the coordinate plane, a circle with radius 5 units is centered at the origin (0,0). A right triangle $\Delta ABC$ has $\angle B = 90^\circ$ and points $B$ and $C$ lie on the circle. The hypotenuse $AC$ of the triangle intersects the circle at points $A$ and $C$. Point $D$ is the midpoint of the hypotenuse $AC$. Determine the area of triangle $\Delta ABD$. Let's think step by step and output the final answer within \boxed{}.
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