Let $AD$ be the angle bisector of triangle $ABC$, and let the line $\ell$ touch circumcircles of triangles $ADB$ and $ADC$ at points $M$ and $N$ accordingly. Prove that the circle passing through the midpoints of the segments $BD$, $DC$ and $MN$ is tangent to the line $\ell$.
Problem
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Tags: geometry, tangent
soryn
27.09.2024 14:26
All Russian MO in 2024?
parmenides51
27.09.2024 15:06
Finals + Regional Both collected inside Russia Contests
soryn
27.09.2024 15:24
I really don't see it
parmenides51
27.09.2024 15:27
try to open the links using a different browser (google chrome or firefox)
soryn
27.09.2024 15:44
The link is opened, but,I don't see this problem
parmenides51
27.09.2024 16:47
Problem is from year 2001 and not 2024, post. Collection is here Post collection might not be yet in related forum collection, as I have asked here for aops admins to add it.