IMO Shortlist 1990 problem 9
Dodao/la:
arhiva2. travnja 2012. The incenter of the triangle
is
The midpoint of
is
and that of
is
The lines
and
meet at
the lines
and
at
If the areas of the triangles
and
are equal, what is the measure of angle
%V0
The incenter of the triangle $ABC$ is $K.$ The midpoint of $AB$ is $C_1$ and that of $AC$ is $B_1.$ The lines $C_1K$ and $AC$ meet at $B_2,$ the lines $B_1K$ and $AB$ at $C_2.$ If the areas of the triangles $AB_2C_2$ and $ABC$ are equal, what is the measure of angle $\angle CAB?$
Izvor: Međunarodna matematička olimpijada, shortlist 1990
Školjka 
