← etc / Encyclopedia of Triangle Centers X1512–X1600 · Orthojoins, Moses Circle Centers & Star-Named Centers / X_1523 ← Prev Overview · Code Next → X1523¶ ORTHOJOIN OF X14 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, 13 }: Central Line L(4, 13) { 1522, 1553 }: Central Line L(1522, 1553) 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_13 = 1st ISOGONIC CENTER (FERMAT POINT, TORRICELLI POINT) (0.5879, 0.2819) X_1522 = ORTHOJOIN OF X(13) (3.2645, -4.0957) X_1553 = ORTHOJOIN OF X(115) (0.5489, 0.7779) X_1523 = ORTHOJOIN OF X(14) (0.6538, 0.5898) A B C X4 X13 X1522 X1553 X1523 (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, 13 }: Central Line L(4, 13) { 1522, 1553 }: Central Line L(1522, 1553) 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_13 = 1st ISOGONIC CENTER (FERMAT POINT, TORRICELLI POINT) (0.6188, 0.2763) X_1522 = ORTHOJOIN OF X(13) (1.1308, -0.8734) X_1553 = ORTHOJOIN OF X(115) (0.6180, 0.8847) X_1523 = ORTHOJOIN OF X(14) (0.6653, 0.7229) A B C X4 X13 X1522 X1553 X1523 (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, 13 }: Central Line L(4, 13) { 1522, 1553 }: Central Line L(1522, 1553) 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_13 = 1st ISOGONIC CENTER (FERMAT POINT, TORRICELLI POINT) (0.6001, 0.2799) X_1522 = ORTHOJOIN OF X(13) (1.0396, -0.8719) X_1553 = ORTHOJOIN OF X(115) (0.6049, 0.9176) X_1523 = ORTHOJOIN OF X(14) (0.6423, 0.7636) A B C X4 X13 X1522 X1553 X1523 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, 13 }: Central Line L(4, 13) { 1522, 1553 }: Central Line L(1522, 1553) 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_13 = 1st ISOGONIC CENTER (FERMAT POINT, TORRICELLI POINT) (0.6324, 0.2733) X_1522 = ORTHOJOIN OF X(13) (0.6344, 0.8176) X_1553 = ORTHOJOIN OF X(115) (0.6331, 1.1246) X_1523 = ORTHOJOIN OF X(14) (0.6334, 1.0413) A B C X4 X13 X1522 X1553 X1523 Kimberling (6, 9, 13) | AB = 1 X1523 (ORTHOJOIN OF X14) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶ Constructed Elements Central Lines: {4, 13}, {1522, 1553} Related Centers: X4 (ORTHOCENTER), X13 (1st ISOGONIC CENTER), X1522 (ORTHOJOIN OF X13), X1553 (ORTHOJOIN OF X115) Trilinears: \(f(a,b,c) : f(b,c,a) : f(c,a,b)\) (see note above X1512) Search Value (6, 9, 13): \(-7.868715493457\) ▸ Incident Central Lines2 lines {4, 13}, {1522, 1553}
