- Cosmin Pohoata, On the Parry reflection point, Forum Geometricorum 8 (2008), 65-70. (Link to the paper’s abstract)
We give a synthetic proof of C. F. Parry’s theorem that the reflections in the sidelines of a triangle of three parallel lines through the vertices are concurrent if and only if they are parallel to the Euler line, the point of concurrency being the Parry reflection point. We also show that the Parry reflection point is common to a triad of circles associated with the tangential triangle and the triangle of reflections (of the vertices in their opposite sides). A dual result is also given, emerging a new triangle center, which lies on the circumcircle of the triangle formed by the Parry reflection point, the orthocenter and the circumcenter of the triangle.
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