X3913

X10com[INVERSE(n(INTOUCH TRIANGLE))]

Let OA be the circle tangent to side BC at its midpoint and to the circumcircle on the same side of BC as A. Define OB and OC cyclically. X3913 is the radical center of the circles OA, OB, OC. See the reference at X1001.
< 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) incircle: Incircle of △ABC { 8, 21 }: Central Line L(8, 21) { 56, 100 }: Central Line L(56, 100) { 65, 224 }: Central Line L(65, 224) { 1, 474 }: Central Line L(1, 474) { 3, 519 }: Central Line L(3, 519) { 4, 528 }: Central Line L(4, 528) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_1 = INCENTER (0.5714, 0.2333) X_8 = NAGEL POINT (0.4694, 0.1333) X_21 = SCHIFFLER POINT (0.5287, 0.1771) X_56 = EXSIMILICENTER(CIRCUMCIRCLE, INCIRCLE) (0.6316, 0.3438) X_100 = ANTICOMPLEMENT OF FEUERBACH POINT (0.1429, 0.4666) X_65 = ORTHOCENTER OF THE INTOUCH TRIANGLE (0.6041, 0.2933) X_224 = -CEVA CONJUGATE OF X(63) (1.2479, 0.4419) X_474 = EULER LINE INTERCEPT OF LINE X(10)X(56) (0.5441, 0.2176) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_519 = ISOGONAL CONJUGATE OF X(106) (0.9566, 0.6107) X_4 = ORTHOCENTER (0.6122, 0.3958) X_528 = DIRECTION OF VECTOR AX + BX + CX, where X = X(11) (1.0237, -0.1286) X_3913 = com[INVERSE(n(INTOUCH TRIANGLE))] (0.7232, 0.3208) A B C X1 X8 X21 X56 X100 X65 X224 X474 X3 X519 X4 X528 X3913 (a, b, c) = (5, 6, 7) | AB = 1

X3913 (X10com[INVERSE(n(INTOUCH TRIANGLE))]) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Barycentrics: \(f(a,b,c) : f(b,c,a) : f(c,a,b)\), where \(f(a,b,c) = a(b + c - a)(a^{2} + ab + ac - 2bc)\)
Search Value (6, 9, 13): \(-5.578018081208\)
▸ Incident Central Lines50 lines

{1, 474}, {2, 3303}, {3, 519}, {4, 528}, {6, 979}, {8, 21}, {10, 1001}, {12, 3434}, {20, 529}, {35, 956}, {36, 3633}, {40, 518}, {43, 1191}, {46, 3555}, {56, 100}, {65, 224}, {72, 2900}, {78, 3057}, {81, 2334}, {200, 960}, {218, 1018}, {220, 3208}, {341, 3685}, {390, 480}, {404, 3241}, {405, 3679}, {497, 1329}, {521, 3157}, {535, 1657}, {950, 1260}, {978, 1616}, {986, 3242}, {993, 3625}, {999, 3244}, {1104, 3749}, {1279, 1722}, {1320, 1392}, {1466, 3476}, {1482, 2802}, {1621, 3617}, {2082, 3693}, {2264, 3692}, {2269, 3713}, {2478, 3058}, {2550, 2894}, {2886, 3085}, {2975, 3621}, {3035, 3086}, {3243, 3339}, {3698, 3748}

▸ Functional Relations2 relations