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orthocenter of ABC is also orthocenter of DEF

Source: Mathematics Regional Olympiad of Mexico West 2018 P5

September 8, 2022
geometryorthocenter

Problem Statement

Let ABCABC be a scalene triangle, Γ\Gamma its circumscribed circle and HH the point where the altitudes of triangle ABCABC meet. The circumference with center at HH passing through AA cuts Γ\Gamma at a second point DD. In the same way, the circles with center at HH and passing through BB and CC cut Γ\Gamma again at points EE and FF, respectively. Prove that HH is also the point in which the altitudes of the triangle DEFDEF meet.
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