MathDB

5

Part of 2009 Ukraine Team Selection Test

Problems(1)

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

Source: Ukraine TST 2009 p4

5/2/2020
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.
geometrycircumcircleCircumcenterright triangleorthocenter