IMO 1976 LL USA39

In riangleABC, the inscribed circle is tangent to side BC at X.

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IMO 1976 LL USA39

Origin: USA

Problem

In \triangleABC, the inscribed circle is tangent to side BC at X. Segment AX is drawn. Prove that the line joining the midpoint of segment AX to the midpoint of side BC passes through the center I of the inscribed circle.