MathDB
<BAK = <CAL wanted, 3 midpoints, centroid, 2 circumcircles,

Source: 2023 Grand Duchy of Lithuania, MC p3 (Baltic Way TST)

March 23, 2024
geometrycircumcircleincenter

Problem Statement

The midpoints of the sides BCBC, CACA and ABAB of triangle ABCABC are MM, NN and PP respectively . GG is the intersection point of the medians. The circumscribed circle around BGPBGP intersects the line MPMP at the point KK (different than PP).The circle circumscribed around CGNCGN intersects the line MNMN at point LL (different than NN). Prove that ∠BAK=∠CAL\angle BAK = \angle CAL.
Back to ProblemsView on AoPS