← etc / Encyclopedia of Triangle Centers X1512–X1600 · Orthojoins, Moses Circle Centers & Star-Named Centers / X_1554 ← Prev Overview · Code Next → X1554¶ ORTHOJOIN OF X125 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) { 30, 113 }: Central Line L(30, 113) { 132, 1503 }: Central Line L(132, 1503) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_30 = EULER INFINITY POINT (0.7469, 0.7481) X_113 = JERABEK ANTIPODE (0.4319, 0.4718) X_132 = ∩X(4)X(32) (0.5642, 0.5039) X_1503 = POINT ARKAB (0.4818, -0.3843) X_1554 = ORTHOJOIN OF X(125) (0.6041, 0.9223) A B C X30 X113 X132 X1503 X1554 (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) { 30, 113 }: Central Line L(30, 113) { 132, 1503 }: Central Line L(132, 1503) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6400, 0.4800) X_30 = EULER INFINITY POINT (0.7077, 0.7120) X_113 = JERABEK ANTIPODE (0.5000, 0.4800) X_132 = ∩X(4)X(32) (0.6400, 0.4800) X_1503 = POINT ARKAB (0.5467, -0.4150) X_1554 = ORTHOJOIN OF X(125) (0.6400, 0.9600) A B C X30 X113 X132 X1503 X1554 (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) { 30, 113 }: Central Line L(30, 113) { 132, 1503 }: Central Line L(132, 1503) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6180, 0.4859) X_30 = EULER INFINITY POINT (0.6751, 0.7207) X_113 = JERABEK ANTIPODE (0.5000, 0.4859) X_132 = ∩X(4)X(32) (0.6180, 0.4859) X_1503 = POINT ARKAB (0.5393, -0.4130) X_1554 = ORTHOJOIN OF X(125) (0.6180, 0.9717) A B C X30 X113 X132 X1503 X1554 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) { 30, 113 }: Central Line L(30, 113) { 132, 1503 }: Central Line L(132, 1503) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6331, 0.2801) X_30 = EULER INFINITY POINT (0.6229, 0.7447) X_113 = JERABEK ANTIPODE (0.5653, 0.5626) X_132 = ∩X(4)X(32) (0.6532, 0.5491) X_1503 = POINT ARKAB (0.5683, -0.5623) X_1554 = ORTHOJOIN OF X(125) (0.6324, 1.1190) A B C X30 X113 X132 X1503 X1554 Kimberling (6, 9, 13) | AB = 1 X1554 (ORTHOJOIN OF X125) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶ Constructed Elements Central Lines: {30, 113}, {132, 1503} Related Centers: X30 (EULER INFINITY POINT), X113 (JERABEK ANTIPODE), X132 (∩X4X32), X1503 (POINT ARKAB) Trilinears: \(f(a,b,c) : f(b,c,a) : f(c,a,b)\) (see note above X1512) Search Value (6, 9, 13): \(-8.662687324012\) ▸ Incident Central Lines2 lines {30, 113}, {132, 1503}
