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TOT 195 1988 Autumn Train S2 three equal circumcircles of triangles

Source:

March 7, 2021
geometrycircumcirclecircumradiusorthocenter

Problem Statement

Let NN be the orthocentre of triangle ABCABC (i .e. the point where the altitudes meet). Prove that the circumscribed circles of triangles ABN,ACNABN, ACN and BCNBCN each have equal radius.
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