15

Part of 2014 Sharygin Geometry Olympiad

Problems(1)

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

Source: Sharygin Geometry Olympiad 2014 Correspondence Round P15

ABC

be a non-isosceles triangle. The altitude from

A

, the bisector from

B

and the median from

C

concur at point

K

. a) Which of the sidelengths of the triangle is medial (intermediate in length)? b) Which of the lengths of segments

AK, BK, CK

is medial (intermediate in length)?

geometryconcurrencyconcurrent