In triangle
, let
be the center of the excircle tangent to side
at
and to the extensions of the sides
and
at
and
respectively. Suppose that the lines
and
are perpendicular and intersect at
. Let
be the foot of the perpendicular from
to line
. Determine the angles
and
.
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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 $\angle{AEB_{1}}$.
Školjka