*Using the same construction above, instead of G, we can also use X(20)-DeLongchamp's point. Let ABC be a triangle and L a line passing through the DeLongchamp's X(20). Denote: A' = the reflection of A in L A'b, A'c = the reflections of A' in AC, AB, resp. Similarly B'c, B'a and C'a, C'b A*B*C* = the triangle bounded by A'bA'c, B'cB'a, C'aC'b Then the circumcircle of A*B*C* touches the line L at a point T. T is the orthogonal projection of the orthocenter H on the line L.
*Using the same construction above, instead of G, we can also use X(20)-DeLongchamp's point.
ReplyDeleteLet ABC be a triangle and L a line passing through the DeLongchamp's X(20). Denote: A' = the reflection of A in L A'b, A'c = the reflections of A' in AC, AB, resp. Similarly B'c, B'a and C'a, C'b A*B*C* = the triangle bounded by A'bA'c, B'cB'a, C'aC'b Then the circumcircle of A*B*C* touches the line L at a point T. T is the orthogonal projection of the orthocenter H on the line L.
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