TITLE: Triangle related coordinate geometry question
QUESTION [2 upvotes]: 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.

REPLY [2 votes]: Hint: Here is a diagram of the construction described above.
$\hspace{4.5cm}$
There is no absolute scale given in the problem, so lets set the inradius of $\triangle ABC$ to be $1$. Since the radius of the excircle opposite $A$ is twice that of the incircle, it is $2$. By similar triangles, we have $|AE|=2|AD|$. Furthermore, $|DE|=3$, so $|AD|=3$ and $|AE|=6$.
Everything else should be calculable using similar triangles.
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