IMO Shortlist 1967 problem 1
Dodao/la:
arhiva2. travnja 2012. ![A_0B_0C_0](/media/m/2/2/8/228fe44bdf25412042ad4e341ab9d39b.png)
and
![A_1B_1C_1](/media/m/1/a/f/1af9d15fbb4b582c4f99670f42359e2d.png)
are acute-angled triangles. Describe, and prove, how to construct the triangle
![ABC](/media/m/a/c/7/ac75dca5ddb22ad70f492e2e0a153f95.png)
with the largest possible area which is circumscribed about
![A_0B_0C_0](/media/m/2/2/8/228fe44bdf25412042ad4e341ab9d39b.png)
(so
![BC](/media/m/5/0/0/5005d4d5eac1b420fbabb76c83fc63ad.png)
contains
![B_0, CA](/media/m/e/c/b/ecb7f729b9a5b7df7deafc706d080685.png)
contains
![B_0](/media/m/5/a/7/5a7b148f9ae7eef70595a0deebfddd3a.png)
, and
![AB](/media/m/5/2/9/5298bd9e7bc202ac21c423e51da3758e.png)
contains
![C_0](/media/m/e/9/e/e9eb7207b3e27429b1d887f6793224be.png)
) and similar to
%V0
$A_0B_0C_0$ and $A_1B_1C_1$ are acute-angled triangles. Describe, and prove, how to construct the triangle $ABC$ with the largest possible area which is circumscribed about $A_0B_0C_0$ (so $BC$ contains $B_0, CA$ contains $B_0$, and $AB$ contains $C_0$) and similar to $A_1B_1C_1.$
Izvor: Međunarodna matematička olimpijada, shortlist 1967