parmenides51 wrote: Let $s$ be the circumcircle of triangle $ABC, L$ and $W$ be common points of angle's $A$ bisector with side $BC$ and $s$ respectively, $O$ be the circumcenter of triangle $ACL$. Restore triangle $ABC$, if circle $s$ and points $W$ and $O$ are given. (D.Prokopenko) Denote by $W^A$ the intersection of circumcircle of $ABC$ od the perpendicular bisection of $BC$. Then points $W^A$, $O$ and $C$ are colinear, because $WC$ is the tangent line to the circumcircle of $ALC$. Hence we should just take the intersection of $s$ with $W^AO$, this will be the vertex $C$. Point $B$ is symmetric to $C$ with respect to $WW^A$, and $A$ is the intersection of $s$ and the circle centered in $O$ and radius $OC$.