MathDB
2012-2013 Winter OMO #49

Source:

January 16, 2013
Online Math Opengeometryanalytic geometry

Problem Statement

In △ABC\triangle ABC, CA=19602CA=1960\sqrt{2}, CB=6720CB=6720, and ∠C=45∘\angle C = 45^{\circ}. Let KK, LL, MM lie on BCBC, CACA, and ABAB such that AK⊥BCAK \perp BC, BL⊥CABL \perp CA, and AM=BMAM=BM. Let NN, OO, PP lie on KLKL, BABA, and BLBL such that AN=KNAN=KN, BO=COBO=CO, and AA lies on line NPNP. If HH is the orthocenter of △MOP\triangle MOP, compute HK2HK^2. [hide="Clarifications"]
[*] Without further qualification, ``XYXY'' denotes line XYXY.
Evan Chen
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