MathDB

3

Part of 2001 Mexico National Olympiad

Problems(1)

Mexican cyclic quadrilateral

Source: Mexican Mathematical Olympiad 2001 OMM P3

7/30/2018
ABCDABCD is a cyclic quadrilateral. MM is the midpoint of CDCD. The diagonals meet at PP. The circle through PP which touches CDCD at MM meets ACAC again at RR and BDBD again at QQ. The point SS on BDBD is such that BS=DQBS = DQ. The line through SS parallel to ABAB meets ACAC at TT. Show that AT=RCAT = RC.
geometrycyclic quadrilateralequal segments