IMO Shortlist 1982 problem 20
Dodao/la:
arhiva2. travnja 2012. Let
![ABCD](/media/m/9/c/e/9ce25711ba18d9663b73c3580de4bf5a.png)
be a convex quadrilateral and draw regular triangles
![ABM, CDP, BCN, ADQ](/media/m/2/8/8/288789c25a757613a6b821260d9f8605.png)
, the first two outward and the other two inward. Prove that
![MN = AC](/media/m/8/e/5/8e5926279266906fc6ded98519d89f37.png)
. What can be said about the quadrilateral
![MNPQ](/media/m/7/4/a/74aafacb841213f440a2ccfc75aad569.png)
?
%V0
Let $ABCD$ be a convex quadrilateral and draw regular triangles $ABM, CDP, BCN, ADQ$, the first two outward and the other two inward. Prove that $MN = AC$. What can be said about the quadrilateral $MNPQ$?
Izvor: Međunarodna matematička olimpijada, shortlist 1982