Geometry Level 3

In a triangle $$PQR$$, $$\angle R = 90^\circ$$.

If $$\tan \frac{P}{2}$$ and $$\tan \frac{Q}{2}$$ are the roots of $$ax^2 + bx + c = 0$$, where $$a\ne 0$$, then which of the following is true?

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