Symmetric_triangles2

Conic trhough vertices of symmetric triangles

There is a conic passing through the six vertices of two symmetric (with respect to a point X) triangles. Switch to the selection-tool (CTRL+1). Catch and modify the vertices of ABC or point X. This proposition is a special case of a more general on perspective triangles. Look at the file Symmetric_triangles3.html .

Drawing the lines: AI parallel to BC, IA' parallel to CB', FC parallel to AB and EF parallel to BA' we define a complete quadrilateral (q) having sides the lines intersecting at I and F. The conic coincides with the [nine-point-conic] of the quadrilateral. In addition to {A,B,C,A',B',C'} which become side-middles of the quadrilateral (q), the conic passes through the points F, H, I (see NinePointsConic.html ).

Conic trhough vertices of symmetric triangles

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