Let $ABC$ be a triangle for which the tangent from $A$ to the circumcircle intersects line $BC$ at $D$, and let $O$ be the circumcenter. Construct the line $l$ that passes through $A$ and is perpendicular to $OD$. $l$ intersects $OD$ at $E$ and $BC$ at $F$. Let the circle passing through $ADO$ intersect $BC$ again at $H$. It is given that $AD=AO=1$. a) Find $OE$ b) Suppose for this part only that $FH=\frac{1}{\sqrt{12}}$: determine the area of triangle $OEF$. c) Suppose for this part only that $BC=\sqrt3$: determine the area of triangle $OEF$. d) Suppose that $B$ lies on the angle bisector of $DEF$. Find the area of the triangle $OEF$.
Attachments:
