IMO Shortlist 1967 problem 6
Dodao/la:
arhiva2. travnja 2012. A line
![l](/media/m/e/e/9/ee975101080f37986f56baaf4c3cdcd2.png)
is drawn through the intersection point
![H](/media/m/4/c/0/4c0872a89da410a25f00b86366efece7.png)
of altitudes of acute-angle triangles. Prove that symmetric images
![l_a, l_b, l_c](/media/m/9/6/5/965012d1d8a60c42dd102e5b1cf9831e.png)
of
![l](/media/m/e/e/9/ee975101080f37986f56baaf4c3cdcd2.png)
with respect to the sides
![BC,CA,AB](/media/m/9/8/c/98c204ffa459114826231180fce7ec09.png)
have one point in common, which lies on the circumcircle of
%V0
A line $l$ is drawn through the intersection point $H$ of altitudes of acute-angle triangles. Prove that symmetric images $l_a, l_b, l_c$ of $l$ with respect to the sides $BC,CA,AB$ have one point in common, which lies on the circumcircle of $ABC.$
Izvor: Međunarodna matematička olimpijada, shortlist 1967