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Geometry Mathley 13.2 Euler line of ABC is Newton line of PQRS

Source:

June 7, 2020
Euler LineNewton linegeometryexcircleEuler Circle

Problem Statement

In a triangle ABCABC, the nine-point circle (N)(N) is tangent to the incircle (I)(I) and three excircles (Ia),(Ib),(Ic)(I_a), (I_b), (I_c) at the Feuerbach points F,Fa,Fb,FcF, F_a, F_b, F_c. Tangents of (N)(N) at F,Fa,Fb,FcF, F_a, F_b, F_c bound a quadrangle PQRSPQRS. Show that the Euler line of ABCABC is a Newton line of PQRSPQRS.
Luis González