1 of distances AM, BM, CM is equal to sum of 2 other distances.
Source: TOT 356 1992 Autumn O S5 - Tournament of Towns
June 10, 2024
geometry
Problem Statement
The bisector of the angle of triangle intersects its circumscribed circle at the point . Suppose is the point symmetric to the incentre of the triangle with respect to the midpoint of the side , and is the second intersection point of the line with the circumscribed circle. Prove that one of the distances , , is equal to the sum of two other distances.(VO Gordon)