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A altitude, B bisector, and C median are concurrent, lengths comparison

Source: Sharygin Geometry Olympiad 2014 Correspondence Round P15

August 1, 2018
geometryconcurrencyconcurrent

Problem Statement

Let ABCABC be a non-isosceles triangle. The altitude from AA, the bisector from BB and the median from CC concur at point KK. a) Which of the sidelengths of the triangle is medial (intermediate in length)? b) Which of the lengths of segments AK,BK,CKAK, BK, CK is medial (intermediate in length)?
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