Problem

Source: 2021 Yasinsky Geometry Olympiad X-XI advanced p1, X-XI p4

Tags: geometry, angle bisector, circumcircle



Let $BF$ and $CN$ be the altitudes of the acute triangle $ABC$. Bisectors the angles $ACN$ and $ABF$ intersect at the point $T$. Find the radius of the circle circumscribed around the triangle $FTN$, if it is known that $BC = a$. (Grigory Filippovsky)