MathDB

515

Part of 1990 All Soviet Union Mathematical Olympiad

Problems(1)

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

Source:

8/14/2019
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".
geometrySegmentProduct