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Iran NMO 2008 (Second Round) - Problem6

Source:

September 22, 2010
geometrycircumcircletrigonometry

Problem Statement

In triangle ABCABC, HH is the foot of perpendicular from AA to BCBC. OO is the circumcenter of ΔABC\Delta ABC. T,T′T,T' are the feet of perpendiculars from HH to AB,ACAB,AC, respectively. We know that AC=2OTAC=2OT. Prove that AB=2OT′AB=2OT'.
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