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5

Part of 2007 Paraguay Mathematical Olympiad

Problems(1)

Paraguayan National Olympiad 2007, Level 3, Problem 5

Source:

9/1/2014
Let A,B,C,A, B, C, be points in the plane, such that we can draw 33 equal circumferences in which the first one passes through AA and BB, the second one passes through BB and CC, the last one passes through CC and AA, and all 33 circumferences share a common point PP. Show that the radius of each of these circumferences is equal to the circumradius of triangle ABCABC, and that PP is the orthocenter of triangle ABCABC.
geometrycircumcircle