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triangle of orthocenters is right, AC=BD=CE=DO, O circumcenter of ABCDE

Source: Ukraine TST 2009 p4

May 2, 2020
geometrycircumcircleCircumcenterright triangleorthocenter

Problem Statement

Let A,B,C,D,EA,B,C,D,E be consecutive points on a circle with center OO such that AC=BD=CE=DOAC=BD=CE=DO. Let H1,H2,H3H_1,H_2,H_3 be the orthocenters triangles ACD,BCD,BCEACD,BCD,BCE respectively. Prove that the triangle H1H2H3H_1H_2H_3 is right.
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