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ARMO 2019 9.6

Source: All-Russian Math Olympiad 2019

July 12, 2019
ARMO

Problem Statement

There is point DD on edge ACAC isosceles triangle ABCABC with base BCBC. There is point KK on the smallest arc CDCD of circumcircle of triangle BCDBCD. Ray CKCK intersects line parallel to line BCBC through AA at point TT. Let MM be midpoint of segment DTDT. Prove that ∠AKT=∠CAM\angle AKT=\angle CAM.
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