In triangle
![ABC](/media/m/a/c/7/ac75dca5ddb22ad70f492e2e0a153f95.png)
, let
![J](/media/m/9/0/e/90ef5cc2558381e341da5808eb92126f.png)
be the center of the excircle tangent to side
![BC](/media/m/5/0/0/5005d4d5eac1b420fbabb76c83fc63ad.png)
at
![A_{1}](/media/m/9/7/4/9742b2655cd943b758073e1f1d090c23.png)
and to the extensions of the sides
![AC](/media/m/6/4/7/647ef3a5d68f07d59d84afe03a9dc655.png)
and
![AB](/media/m/5/2/9/5298bd9e7bc202ac21c423e51da3758e.png)
at
![B_{1}](/media/m/f/a/5/fa55cf39f6736c287bf64ee9471f00f1.png)
and
![C_{1}](/media/m/e/4/6/e46111370b6102ad343bcdc7190d9ff9.png)
respectively. Suppose that the lines
![A_{1}B_{1}](/media/m/1/e/3/1e3da87377af3294fc47baebb418ed55.png)
and
![AB](/media/m/5/2/9/5298bd9e7bc202ac21c423e51da3758e.png)
are perpendicular and intersect at
![D](/media/m/7/0/0/7006c4b57335ab717f8f20960577a9ef.png)
. Let
![E](/media/m/8/b/0/8b01e755d2253cb9a52f9e451d89ec11.png)
be the foot of the perpendicular from
![C_{1}](/media/m/e/4/6/e46111370b6102ad343bcdc7190d9ff9.png)
to line
![DJ](/media/m/c/5/7/c5757e143a5baf1dca29bdd5851d2065.png)
. Determine the angles
![\angle{BEA_{1}}](/media/m/e/8/6/e86c40e97c7c733279b578845b6307b4.png)
and
![\angle{AEB_{1}}](/media/m/b/c/6/bc6547a388c939dcc98e3e9090da112b.png)
.
%V0
In triangle $ABC$, let $J$ be the center of the excircle tangent to side $BC$ at $A_{1}$ and to the extensions of the sides $AC$ and $AB$ at $B_{1}$ and $C_{1}$ respectively. Suppose that the lines $A_{1}B_{1}$ and $AB$ are perpendicular and intersect at $D$. Let $E$ be the foot of the perpendicular from $C_{1}$ to line $DJ$. Determine the angles $\angle{BEA_{1}}$ and $\angle{AEB_{1}}$.