MathDB

5

Part of 2007 Czech and Slovak Olympiad III A

Problems(1)

the orthocenter of a triangle

Source: Czech and Slovak third round,2007,p5

3/3/2012
In an acute-angled triangle ABCABC (AC≠BCAC\ne BC), let DD and EE be points on BCBC and ACAC, respectively, such that the points A,B,D,EA,B,D,E are concyclic and ADAD intersects BEBE at PP. Knowing that CP⊥ABCP\bot AB, prove that PP is the orthocenter of triangle ABCABC.
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