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X₃₈₂₂¶

X₂₀₉₉com(3rd EULER TRIANGLE)

Suppose that ABC is an acute triangle. Let L_A be the circle that is externally tangent to the nine-point circle and to the sidelines AB and AC. Define L_B and L_C cyclically. The three circles are here named the Odehnal tritangent circles. Their radical center is X₃₈₂₂. The center of the Apollonian circle of L_A, L_B, L_C is X₆₁₆₇. (Boris Odehnal, “A Triad of Tritangent Circles, Journal for Geometry and Graphics 18 (2014) no. 1, 61-71)

X₃₈₂₂ (X₂₀₉₉com(3rd EULER TRIANGLE)) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_3822 = X_2099com(3rd EULER TRIANGLE)."""

        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,
            promote_point_to_top,
            spieker_center_of,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_03822(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_3822 = X_2099com(3rd EULER TRIANGLE) on reference triangle ABC."""
            X_3822 = eval_barycentric_point(model, A, B, C, '(b + c)*(b**(3) + c**(3) - a**(2)*b - a**(2)*c - b**(2)*c - b*c**(2) - a*b*c)', ID="X_3822", classes=["selected", "target"])
            X_10 = spieker_center_of(model, A, B, C, ID="X_10", classes=["center", "incident"])
            X_12 = eval_trilinear_point(model, A, B, C, '1 + cos(B - C)', ID="X_12", classes=["center", "incident"])
            central_line(model, X_10, X_12, 10, 12, incident=True)
            X_2 = centroid_of(model, A, B, C, ID="X_2", classes=["center", "incident"])
            X_36 = eval_trilinear_point(model, A, B, C, '1 - 2*cos(A)', ID="X_36", classes=["center", "incident"])
            central_line(model, X_2, X_36, 2, 36, incident=True)
            X_37 = eval_trilinear_point(model, A, B, C, 'b + c', ID="X_37", classes=["center", "incident"])
            X_115 = eval_trilinear_point(model, A, B, C, 'b*c*(b**(2) - c**(2))**(2)', ID="X_115", classes=["center", "incident"])
            central_line(model, X_37, X_115, 37, 115, incident=True)
            return promote_point_to_top(model, X_3822)


        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_3822 on the given reference triangle."""
            model = create_model('X_3822 = X_2099com(3rd EULER TRIANGLE)')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_03822(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-03822.json"))
            write_center_svg(
                model_acute,
                here / "x-03822.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X3822¶

X₃₈₂₂¶