← etc / Encyclopedia of Triangle Centers

X₁₉₉₇¶

ORTHOCORRESPONDENT OF X₈

X₁₉₉₇ (ORTHOCORRESPONDENT OF X₈) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_1997 = ORTHOCORRESPONDENT OF X_8."""

        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_barycentric_point,
            eval_trilinear_point,
            intersect_lines,
            promote_point_to_top,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_01997(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_1997 = ORTHOCORRESPONDENT OF X_8 on reference triangle ABC."""
            X_2 = centroid_of(model, A, B, C, ID="X_2", classes=["center"])
            X_37 = eval_trilinear_point(model, A, B, C, 'b + c', ID="X_37", classes=["center"])
            X_1210 = eval_barycentric_point(model, A, B, C, 'a**(3)*(b + c) - a**(2)*(b - c)**(2) - a*(b - c)**(2)*(b + c) + (b**(2) - c**(2))**(2)', ID="X_1210", classes=["center"])
            X_1265 = eval_trilinear_point(model, A, B, C, '((cos(A))*((csc(A/2))**(4)))', ID="X_1265", classes=["center"])
            central_line(model, X_2, X_37, 2, 37)
            central_line(model, X_1210, X_1265, 1210, 1265)
            X_1997 = intersect_lines(model, X_2, X_37, X_1210, X_1265, ID="X_1997", classes=["selected", "target"])
            return promote_point_to_top(model, X_1997)


        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_1997 on the given reference triangle."""
            model = create_model('X_1997 = ORTHOCORRESPONDENT OF X_8')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_01997(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-01997.json"))
            write_center_svg(
                model_acute,
                here / "x-01997.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X1997¶

X₁₉₉₇¶