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perimeter of ABC = k (BC)

Source: IV Soros Olympiad 1997-98 R3 11.10 https://artofproblemsolving.com/community/c2416727_soros_olympiad_in_mathematics

June 2, 2024
geometryperimeterratio

Problem Statement

The perimeter of triangle ABCABC is kk times larger than side BCBC, AB≠ACAB \ne AC. In what ratio does the median to side BCBC divide the diameter of the circle inscribed in this triangle, perpendicular to this side?
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