X2975

INSIMILICENTER(CIRCUMCIRCLE, AC-INCIRCLE)

X2975 is the insimilicenter(circumcircle, ac-incircle).
< 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) { 3, 8 }: Central Line L(3, 8) { 2, 12 }: Central Line L(2, 12) { 1, 21 }: Central Line L(1, 21) { 10, 36 }: Central Line L(10, 36) { 28, 92 }: Central Line L(28, 92) { 54, 72 }: Central Line L(54, 72) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_8 = NAGEL POINT (0.4694, 0.1333) X_2 = CENTROID (0.5374, 0.2000) X_12 = {X(1),X(5)}-HARMONIC CONJUGATE OF X(11) (0.5641, 0.2407) X_1 = INCENTER (0.5714, 0.2333) X_21 = SCHIFFLER POINT (0.5287, 0.1771) X_10 = SPIEKER CENTER (0.5204, 0.1833) X_36 = INVERSE-IN-CIRCUMCIRCLE OF INCENTER (1.3333, 1.6330) X_28 = CEVAPOINT OF X(19) AND X(25) (0.6285, 0.4382) X_92 = CEVAPOINT OF INCENTER AND CLAWSON POINT (0.5949, 0.3639) X_54 = KOSNITA POINT (0.5880, 0.2176) X_72 = ISOGONAL CONJUGATE OF X(28) (0.4367, 0.0733) X_2975 = INSIMILICENTER(CIRCUMCIRCLE, AC-INCIRCLE) (0.4840, 0.1184) A B C X3 X8 X2 X12 X1 X21 X10 X36 X28 X92 X54 X72 X2975 (a, b, c) = (5, 6, 7) | AB = 1

X2975 (INSIMILICENTER(CIRCUMCIRCLE, AC-INCIRCLE)) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(f(a,b,c) : f(b,c,a) : f(c,a,b)\), where \(f(a,b,c) = a^{3} + a(bc - b^{2} - c^{2}) - bc(b + c)\)
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(5.219778528225\)
▸ Linear Combinations1 combination
▸ Incident Central Lines41 lines

{1, 21}, {2, 12}, {3, 8}, {9, 604}, {10, 36}, {20, 2894}, {28, 92}, {35, 519}, {48, 2287}, {54, 72}, {55, 145}, {75, 1444}, {78, 947}, {105, 330}, {110, 1098}, {144, 1001}, {172, 1107}, {198, 391}, {229, 409}, {238, 1201}, {329, 405}, {333, 1610}, {348, 934}, {411, 515}, {518, 2330}, {593, 2363}, {596, 759}, {668, 1078}, {672, 2329}, {908, 1125}, {943, 2320}, {950, 1005}, {960, 1319}, {962, 1012}, {966, 2178}, {995, 1724}, {1457, 1935}, {1470, 1788}, {1478, 2476}, {1761, 1953}, {2475, 2886}

▸ Functional Relations9 relations

Notes

The term “AC-incircle” is introduced for “anticomplement of the incircle” by Peter Moses (Dec. 2, 2004). Thus, the AC-incircle is the incircle of the anticomplementary triangle; the circle has center X8 and radius 2r. The exsimilicenter of the circumcircle and AC-incircle is X100, their touchpoint, and the anticomplement of X11.