MathDB

42

Part of 1976 IMO Longlists

Problems(1)

Ratio of lengths being integers.

Source:

1/28/2011
For a point OO inside a triangle ABCABC, denote by A1,B1,C1,A_1,B_1, C_1, the respective intersection points of AO,BO,COAO, BO, CO with the corresponding sides. Let n1=AOA1O,n2=BOB1O,n3=COC1O.n_1 =\frac{AO}{A_1O}, n_2 = \frac{BO}{B_1O}, n_3 = \frac{CO}{C_1O}. What possible values of n1,n2,n3n_1, n_2, n_3 can all be positive integers?
ratiogeometrygeometry unsolved