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Part of 1998 Portugal MO

Problems(1)

Real IMO Shortlist 2019 G2 - Archimedes Broken Chord

Source: https://artofproblemsolving.com/community/c6h1896563p12956114

3/25/2020
Let FF be the midpoint of circle arc ABAB, and let MM be a point on the arc such that AM<MBAM <MB. The perpendicular drawn from point FF on AMAM intersects AMAM at point TT. Show that TT bisects the broken line AMBAMB, that is AT=TM+MBAT =TM+MB.
KöMaL Gy. 2404. (March 1987), Archimedes of Syracuse
geometrychordarc midpointcircle