Another Synthetic Proof of Dao’s Generalization of the Simson Line Theorem
نویسندگان
چکیده
We give a synthetic proof of Dao’s generalization of the Simson line theorem. In [3], Dao Thanh Oai published without proof a remarkable generalization of the Simson line theorem. Theorem 1 (Dao). Let ABC be a triangle with its orthocenter H , let P be an arbitrary point on the circumcircle. Let l be a line through the circumcenter and AP , BP , CP meet l at A1, B1, C1, respectively. Denote A2, B2, C2 the orthogonal projections of A1, B1, C1 onto BC, CA, AB, respectively. Then A2, B2, C2 are collinear and the line passing through A2, B2, C2 bisects PH.
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