IMO Shortlist 1989 problem 18
Dodao/la:
arhiva2. travnja 2012. Given a convex polygon
![A_1A_2 \ldots A_n](/media/m/3/d/b/3dbfe0f5b1f84bfc9be4ee4d64979438.png)
with area
![S](/media/m/c/6/3/c63593c3ec0773fa38c2659e08119a75.png)
and a point
![M](/media/m/f/7/f/f7f312cf6ba459a332de8db3b8f906c4.png)
in the same plane, determine the area of polygon
![M_1M_2 \ldots M_n,](/media/m/3/7/d/37db534e80b7dcdc56a6ebd95d9503b4.png)
where
![M_i](/media/m/e/3/c/e3ca05780cd74a595a0d7131f303c9c8.png)
is the image of
![M](/media/m/f/7/f/f7f312cf6ba459a332de8db3b8f906c4.png)
under rotation
![R^{\alpha}_{A_i}](/media/m/e/6/d/e6d2465c814c1e1196bef9e9569a051d.png)
around
![A_i](/media/m/5/f/0/5f0935569a883b13bb70b83ea33eee14.png)
by
%V0
Given a convex polygon $A_1A_2 \ldots A_n$ with area $S$ and a point $M$ in the same plane, determine the area of polygon $M_1M_2 \ldots M_n,$ where $M_i$ is the image of $M$ under rotation $R^{\alpha}_{A_i}$ around $A_i$ by $\alpha_i, i = 1, 2, \ldots, n.$
Izvor: Međunarodna matematička olimpijada, shortlist 1989