MathDB

3

Part of 2019 Grand Duchy of Lithuania

Problems(1)

<OHC = 90^o wanted, XP + Y Q = AB + XY ,orthocenter, circumcenter

Source: 2019 Grand Duchy of Lithuania, Mathematical Contest p3 (Baltic Way TST)

10/3/2020
Let ABCABC be an acute triangle with orthocenter HH and circumcenter OO. The perpendicular bisector of segment CHCH intersects the sides ACAC and BCBC in points XX and YY , respectively. The lines XOXO and YOYO intersect the side ABAB in points PP and QQ, respectively. Prove that if XP+YQ=AB+XYXP + Y Q = AB + XY then ∠OHC=90o\angle OHC = 90^o.
geometryright angleperpendicularorthocentercircumcircle