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Orthocenter geo

Source: CAPS Match 2023 P5

June 30, 2023
geometry

Problem Statement

Let ABCABC be an acute-angled triangle with orthocenter HH. Let DD be the foot of the altitude from AA to the line BCBC. Let TT be a point on the circle with diameter AHAH such that this circle is internally tangent to the circumcircle of triangle BDTBDT. Let NN be the midpoint of segment AHAH. Prove that BT⊥CNBT \perp CN.
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