← etc / Encyclopedia of Triangle Centers X1512–X1600 · Orthojoins, Moses Circle Centers & Star-Named Centers / X_1548 ← Prev Overview · Code Next → X1548¶ ORTHOJOIN OF X72 5, 6, 7 3, 4, 5 Kepler Kimberling < A B C >: Reference Triangle △ABC [ A B ]: Sideline AB (Base c = 1) [ B C ]: Sideline BC (Side a) [ C A ]: Sideline CA (Side b) { 4, 6 }: Van Aubel Line { 119, 517 }: Central Line L(119, 517) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_4 = ORTHOCENTER (0.6122, 0.3958) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_119 = FEUERBACH ANTIPODE (0.3776, 0.4312) X_517 = ISOGONAL CONJUGATE OF X(104) (0.8180, 0.7154) X_1548 = ORTHOJOIN OF X(72) (0.6661, 0.9613) A B C X4 X6 X119 X517 X1548 (a, b, c) = (5, 6, 7) | AB = 1 < A B C >: Reference Triangle △ABC [ A B ]: Sideline AB (Base c = 1) [ B C ]: Sideline BC (Side a) [ C A ]: Sideline CA (Side b) { 4, 6 }: Van Aubel Line { 119, 517 }: Central Line L(119, 517) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6400, 0.4800) X_4 = ORTHOCENTER (0.6400, 0.4800) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6400, 0.2400) X_119 = FEUERBACH ANTIPODE (0.4200, 0.4400) X_517 = ISOGONAL CONJUGATE OF X(104) (0.8038, 0.6743) X_1548 = ORTHOJOIN OF X(72) (0.6400, 0.8800) A B C X4 X6 X119 X517 X1548 (a, b, c) = (3, 4, 5) | AB = 1 < A B C >: Reference Triangle △ABC [ A B ]: Sideline AB (Base c = 1) [ B C ]: Sideline BC (Side a) [ C A ]: Sideline CA (Side b) { 4, 6 }: Van Aubel Line { 119, 517 }: Central Line L(119, 517) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6180, 0.4859) X_4 = ORTHOCENTER (0.6180, 0.4859) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6180, 0.2429) X_119 = FEUERBACH ANTIPODE (0.4283, 0.4561) X_517 = ISOGONAL CONJUGATE OF X(104) (0.7602, 0.6929) X_1548 = ORTHOJOIN OF X(72) (0.6180, 0.9121) A B C X4 X6 X119 X517 X1548 Kepler (1, √φ, φ) | AB = 1 < A B C >: Reference Triangle △ABC [ A B ]: Sideline AB (Base c = 1) [ B C ]: Sideline BC (Side a) [ C A ]: Sideline CA (Side b) { 4, 6 }: Van Aubel Line { 119, 517 }: Central Line L(119, 517) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6331, 0.2801) X_4 = ORTHOCENTER (0.6331, 0.8294) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6573, 0.1655) X_119 = FEUERBACH ANTIPODE (0.4769, 0.5481) X_517 = ISOGONAL CONJUGATE OF X(104) (0.7243, 0.7243) X_1548 = ORTHOJOIN OF X(72) (0.6245, 1.0660) A B C X4 X6 X119 X517 X1548 Kimberling (6, 9, 13) | AB = 1 X1548 (ORTHOJOIN OF X72) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶ Constructed Elements Central Lines: {4, 6}, {119, 517} Related Centers: X4 (ORTHOCENTER), X6 (SYMMEDIAN POINT), X119 (FEUERBACH ANTIPODE), X517 (ISOGONAL CONJUGATE OF X104) Trilinears: \(f(a,b,c) : f(b,c,a) : f(c,a,b)\) (see note above X1512) Search Value (6, 9, 13): \(-8.053426092880\) ▸ Incident Central Lines2 lines {4, 6}, {119, 517}
