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(356) 5

Part of 1992 Tournament Of Towns

Problems(1)

1 of distances AM, BM, CM is equal to sum of 2 other distances.

Source: TOT 356 1992 Autumn O S5 - Tournament of Towns

6/10/2024
The bisector of the angle AA of triangle ABCABC intersects its circumscribed circle at the point DD. Suppose PP is the point symmetric to the incentre of the triangle with respect to the midpoint of the side BCBC, and MM is the second intersection point of the line PDPD with the circumscribed circle. Prove that one of the distances AMAM, BMBM, CMCM is equal to the sum of two other distances.
(VO Gordon)
geometry