AT-OEMO-REG 2006 Problem 3

In a non isosceles triangle $ABC$ let $w$ be the angle bisector of the exterior angle at $C$ . Let $D$ be the point of intersection of $w$ with the extension of $AB$ . Let $k_A$ be the circumcircle of the triangle $ADC$ and analogy $k_B$ the circumcircle of the triangle $BDC$ . Let $t_A$ be the tangent line to $k_A$ in A and $t_B$ the tangent line to $k_B$ in B. Let $P$ be the point of intersection of $t_A$ and $t_B$ . Given are the points $A$ and $B$ . Determine the set of points $P=P(C )$ over all points $C$ , so that $ABC$ is a non isosceles, acute-angled triangle.