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X₁₂₇₈¶

CONGRUENT MIDWAY-PARALLELIANS POINT

X₁₂₇₈ is the {X₇₅,X₁₉₂}-harmonic conjugate of X₂. For a list of harmonic conjugates, click Tables at the top of this page.

X₁₂₇₈ (CONGRUENT MIDWAY-PARALLELIANS POINT) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_1278 = CONGRUENT MIDWAY-PARALLELIANS POINT."""

        from __future__ import annotations

        from pathlib import Path

        import sympy.geometry as spg
        from geometor.model import Model

        from geometor.etc.ops import (
            central_line,
            centroid_of,
            construct_baseline_triangle,
            create_model,
            eval_trilinear_point,
            nagel_point_of,
            promote_point_to_top,
            reflection_in_point,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_01278(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_1278 = CONGRUENT MIDWAY-PARALLELIANS POINT on reference triangle ABC."""
            X_192 = eval_trilinear_point(model, A, B, C, 'b*c*(c*a + a*b - b*c)', ID="X_192", classes=["center"])
            X_75 = eval_trilinear_point(model, A, B, C, '1/a**(2)', ID="X_75", classes=["center"])
            X_1278 = reflection_in_point(model, X_192, X_75, ID="X_1278", classes=["selected", "target"], guide=False)
            X_2 = centroid_of(model, A, B, C, ID="X_2", classes=["center", "incident"])
            X_37 = eval_trilinear_point(model, A, B, C, 'b + c', ID="X_37", classes=["center", "incident"])
            central_line(model, X_2, X_37, 2, 37, incident=True)
            X_8 = nagel_point_of(model, A, B, C, ID="X_8", classes=["center", "incident"])
            X_726 = eval_trilinear_point(model, A, B, C, '(a **(-3)*(b **(-1) + c **(-1)) - a **(-2)*(b **(-2) + c **(-2)))', ID="X_726", classes=["center", "incident"])
            central_line(model, X_8, X_726, 8, 726, incident=True)
            X_145 = eval_trilinear_point(model, A, B, C, 'b*c*(3*a - b - c)', ID="X_145", classes=["center", "incident"])
            X_740 = eval_trilinear_point(model, A, B, C, 'a **(-2)*(b**(1) + c**(1)) - a**(0)*(b **(-1) + c **(-1))', ID="X_740", classes=["center", "incident"])
            central_line(model, X_145, X_740, 145, 740, incident=True)
            return promote_point_to_top(model, X_1278)


        def build_model(
            sides: tuple[float, float, float] = (5.0, 6.0, 7.0),
            show_guides: bool = False,
        ) -> Model:
            """Build a `geometor.model.Model` for X_1278 on the given reference triangle."""
            model = create_model('X_1278 = CONGRUENT MIDWAY-PARALLELIANS POINT')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_01278(model, A, B, C)
            return model


        if __name__ == "__main__":
            here = Path(__file__).resolve().parent
            model_acute = build_model((5.0, 6.0, 7.0))
            model_acute.save(str(here / "x-01278.json"))
            write_center_svg(
                model_acute,
                here / "x-01278.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X1278¶

X₁₂₇₈¶