MathDB
ASU 515 All Soviet Union MO 1990 abc = a'b'c' = a"b"c", lengths of segments

Source:

August 14, 2019
geometrySegmentProduct

Problem Statement

The point PP lies inside the triangle ABCABC. A line is drawn through PP parallel to each side of the triangle. The lines divide ABAB into three parts length c,c′,c"c, c', c" (in that order), and BCBC into three parts length a,a′,a"a, a', a" (in that order), and CACA into three parts length b,b′,b"b, b', b" (in that order). Show that abc=a′b′c′=a"b"c"abc = a'b'c' = a"b"c".
Back to ProblemsView on AoPS