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X₃₀₀₃¶

(BROCARD AXIS)∩(ORTHIC AXIS)

lies on the cubics K277, K489, K1170, K1171, and these lines: on lines {2, 3260}, {3, 6}, {30, 6128}, {31, 8606}, {37, 7359}, {44, 13006}, {53, 235}, {54, 43753}, {74, 32681}, {111, 9060}, {112, 32710}, {114, 45921}, {115, 11799}, {157, 1974}, {160, 6467}, {186, 8749}, {206, 40947}, {230, 231}, {237, 2393}, {248, 1177}, {393, 847}, {395, 40696}, {396, 40695}, {419, 1632}, {524, 34990}, {607, 2178}, {608, 2164}, {615, 8963}, {648, 44375}, {672, 22059}, {895, 35298}, {1084, 23967}, {1100, 2649}, {1194, 5306}, {1196, 34811}, {1213, 16699}, {1249, 3147}, {1495, 9142}, {1503, 44437}, {1513, 45279}, {1545, 5321}, {1546, 5318}, {1576, 44102}, {1634, 8681}, {1885, 6748}, {1942, 1987}, {1989, 14993}, {2079, 37933}, {2174, 2197}, {2252, 8776}, {2269, 22058}, {2351, 44077}, {2386, 21177}, {2790, 44227}, {3133, 12235}, {3148, 19136}, {3163, 18334}, {3164, 41760}, {3199, 13881}, {3580, 18609}, {3815, 30739}, {4383, 21494}, {4558, 35296}, {5181, 11672}, {5191, 9407}, {5305, 16618}, {5412, 44193}, {5413, 44192}, {5486, 43718}, {5702, 46453}, {6509, 26958}, {6663, 13383}, {7113, 7117}, {7202, 43034}, {7297, 14936}, {7493, 7735}, {7669, 18374}, {7736, 15302}, {7745, 34664}, {8623, 18371}, {8962, 32787}, {9027, 9155}, {9145, 32127}, {9220, 39565}, {9300, 43957}, {9475, 38987}, {9723, 40318}, {9822, 35222}, {9969, 23635}, {10313, 37929}, {11188, 37465}, {11328, 29959}, {13567, 46832}, {14060, 37183}, {14569, 15508}, {14575, 41593}, {14581, 35372}, {14984, 44221}, {15073, 37114}, {15355, 39576}, {16237, 44138}, {16238, 45847}, {17907, 41770}, {18122, 34827}, {18362, 36430}, {18877, 21663}, {19118, 44200}, {20775, 32366}, {21639, 39231}, {23357, 44174}, {23980, 35090}, {34104, 39170}, {34394, 36296}, {34395, 36297}, {35370, 44895}, {35486, 39575}, {36982, 41373}, {37778, 41678}, {39176, 44281}, {40350, 44533}, {40423, 46230}, {41758, 45172}

X₃₀₀₃ ((BROCARD AXIS)∩(ORTHIC AXIS)) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_3003 = (BROCARD AXIS)∩(ORTHIC AXIS)."""

        from __future__ import annotations

        from pathlib import Path

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

        from geometor.etc.ops import (
            construct_baseline_triangle,
            create_model,
            eval_barycentric_point,
            isogonal_conjugate,
            promote_point_to_top,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_03003(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_3003 = (BROCARD AXIS)∩(ORTHIC AXIS) on reference triangle ABC."""
            X_2986 = eval_barycentric_point(model, A, B, C, '1/(1 + cos(2*B) + cos(2*C))', ID="X_2986", classes=["center"])
            X_3003 = isogonal_conjugate(model, A, B, C, X_2986, ID="X_3003", classes=["selected", "target"])
            return promote_point_to_top(model, X_3003)


        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_3003 on the given reference triangle."""
            model = create_model('X_3003 = (BROCARD AXIS)∩(ORTHIC AXIS)')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_03003(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-03003.json"))
            write_center_svg(
                model_acute,
                here / "x-03003.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X3003¶

X₃₀₀₃¶