## Τρίτη, 17 Οκτωβρίου 2017

### 2006 IMO Shortlist G5

In triangle $ABC$, let $J$ be the centre of the excircle tangent to side $BC$ at $A_1$  and to the extensions of sides $AC$ and $AB$ at $B_1$  and $C_1$, respectively.  Suppose that the lines $A_1B_1$ 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 $\angle AEB_1$.

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