IMO Shortlist 1992 problem 11
Dodao/la:
arhiva2. travnja 2012. In a triangle
![ABC,](/media/m/8/a/f/8afcbd6e815ca10256c79a5b310e3d67.png)
let
![D](/media/m/7/0/0/7006c4b57335ab717f8f20960577a9ef.png)
and
![E](/media/m/8/b/0/8b01e755d2253cb9a52f9e451d89ec11.png)
be the intersections of the bisectors of
![\angle ABC](/media/m/c/9/2/c92dca0f4ca20d0ca087b59e09a26fa8.png)
and
![\angle ACB](/media/m/2/b/8/2b827c330f4f220b112b928e106c0a00.png)
with the sides
![AC,AB,](/media/m/2/7/b/27b489bbf3ba3b7e829be6f673a5a575.png)
respectively. Determine the angles
![\angle A,\angle B, \angle C](/media/m/1/d/8/1d8c86033bc344277e7017d931ecdb06.png)
if
%V0
In a triangle $ABC,$ let $D$ and $E$ be the intersections of the bisectors of $\angle ABC$ and $\angle ACB$ with the sides $AC,AB,$ respectively. Determine the angles $\angle A,\angle B, \angle C$ if $\angle BDE = 24 ^{\circ},$ $\angle CED = 18 ^{\circ}.$
Izvor: Međunarodna matematička olimpijada, shortlist 1992