MathDB

2007.11.5

Part of Kyiv City MO Seniors 2003+ geometry

Problems(1)

fixed point for the circumcircle, equal angles (Kyiv City Olympiad 2007 11.5)

Source:

6/29/2020
The points AA and PP are marked on the plane. Consider all such points B,CB, C of this plane that ∠ABP=∠MAB\angle ABP = \angle MAB and ∠ACP=∠MAC\angle ACP = \angle MAC , where MM is the midpoint of the segment BCBC. Prove that all the circumscribed circles around the triangle ABCABC for different points BB and CC pass through some fixed point other than the point AA.
(Alexei Klurman)
geometrycircumcircleequal anglesFixed pointfixed