Given a point A that outside a circle so that $AT$ is tangent to the circle in point $T$
And $AC$ is a secant to that circle in points $B,C$.
From points $B,C$ we build heights to $AT$ in points $D,E$. (point $E$ is between points $D,T$)
$BD=b$, $CE=c$, angle $TAC=\alpha$.
What's the expression of radius $r$ in terms of $b,c,\alpha$?
I'm trying to find a nice solution maybe euclidean or trigonometric/vectors.