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Turkey TST 1992 - P2: Altitude meets circumcircle

Source:

March 13, 2011
geometrycircumcirclegeometry proposed

Problem Statement

The line passing through BB is perpendicular to the side ACAC at EE. This line meets the circumcircle of △ABC\triangle ABC at DD. The foot of the perpendicular from DD to the side BCBC is FF. If OO is the center of the circumcircle of △ABC\triangle ABC, prove that BOBO is perpendicular to EFEF.
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