Given triangle $\triangle ABC$ , with $AB=AC$ and 2 times(length of inradius) which is equal to the length of exradius of excirle opposite vertex $A$. Setup the coordinate system in the plane of triangle $\triangle ABC$ as follow: Origin at vertex $B$, positive X-axis along $BC$ and positive Y-axis on the $A$ side of $BC$. Find the equations of the incircle , excircles and circumcircle.
Also this question is related to the incenter excenter configuration of triangle.I would like to get some help to solve the above question.