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ASU 112 All Soviet Union MO 1968 incircle related

Source:

June 20, 2019
geometryincircle

Problem Statement

The circle inscribed in the triangle ABCABC touches the side [AC][AC] in the point KK. Prove that the line connecting the midpoint of the side [AC][AC] with the centre of the circle halves the segment [BK][BK] .