MathDB

5

Part of 2023 Czech and Slovak Olympiad III A.

Problems(1)

SKMO 2023 P5

Source: czechoslovak national mo round

4/4/2023
In triangle ABCABC let N,M,PN, M, P be the midpoints of the sides BC,CA,ABBC, CA, AB and GG be the centroid of this triangle. Let the circle circumscribed to BGPBGP intersect the line MPMP in point KK, P≠KP \neq K, and the circle circumscribed to CGNCGN intersect the line MNMN in point LL, N≠LN \neq L. Prove that ∠BAK=∠CAL \angle BAK = \angle CAL .
geometry