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# Limit of radius of inscribed circle

Consider the points ,   with . Let be the radius of the inscribed circle of the triangle .

Prove that

Solution

Since we deduce that as . Since the incenter lies on the bisector of , it follows that if is the projection of on the axis

\rho = AD \tan \frac {A}{2}\leq 1\tan \frac {A}{2} \rightarrow 0