Trigonometry or something else?

Geometry Level 4

The A-excircle of triangle $$ABC$$ is defined to be the unique circle which is tangent to lines $$AB$$, $$BC$$ and $$AC$$ of triangle $$ABC$$ which lies on the opposite side of line $$BC$$ as $$A$$.

Triangle $$ABC$$ has side lengths $$BC = 98$$, $$AC = 76$$, $$AB = 54$$, and its A-excircle is tangent to line $$AC$$ at $$D$$. Find the length of $$CD$$ up to three decimal places.

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