IMO 1989 LL INA48

Let S be the point of intersection of the two lines l1 : 7x−5y +

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IMO 1989 LL INA48

Origin: INA

Problem

Let S be the point of intersection of the two lines l1 : 7x−5y + 8 = 0 and l2 : 3x + 4y −13 = 0. Let P = (3, 7), Q = (11, 13), and let A and B be points on the line PQ such that P is between A and Q, and B is between P and Q, and such that PA/AQ = PB/BQ = 2/3. Without finding the coordinates of B find the equations of the lines SA and SB.