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3

Part of 2009 Regional Competition For Advanced Students

Problems(1)

Show that three lines don't intersect in one point

Source: 40th Austrian Mathematical Olympiad 2009, round 1, problem 3

8/5/2009
Let D D, E E, F F be the feet of the altitudes wrt sides BC BC, CA CA, AB AB of acute-angled triangle △ABC \triangle ABC, respectively. In triangle △CFB \triangle CFB, let P P be the foot of the altitude wrt side BC BC. Define Q Q and R R wrt triangles △ADC \triangle ADC and △BEA \triangle BEA analogously. Prove that lines AP AP, BQ BQ, CR CR don't intersect in one common point.
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