X2101

REFLECTION OF X1 IN X1114

X2101 is the reflection of X1 in X1114.
< 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) { 1, 1114 }: Central Line L(1, 1114) { 30, 40 }: Central Line L(30, 40) { 165, 1113 }: Central Line L(165, 1113) { 1312, 1698 }: Central Line L(1312, 1698) { 1313, 1699 }: Central Line L(1313, 1699) 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_1114 = 2nd EULER-LINE-CIRCUMCIRCLE INTERSECTION (0.3178, -0.3746) X_30 = EULER INFINITY POINT (0.7469, 0.7481) X_40 = BEVAN POINT (0.4286, -0.0292) X_165 = CENTROID OF THE EXCENTRAL TRIANGLE (0.4762, 0.0583) X_1113 = 1st EULER-LINE-CIRCUMCIRCLE INTERSECTION (0.6822, 0.5787) X_1312 = 1st MOSES INTERSECTION (0.6472, 0.4872) X_1698 = INSIMILICENTER(BEVAN CIRCLE, NINE-POINTCIRCLE) (0.5306, 0.1933) X_1313 = 2nd MOSES INTERSECTION (0.4650, 0.0106) X_1699 = EXSIMILICENTER(BEVAN CIRCLE, NINE-POINT CIRCLE) (0.5986, 0.3416) X_2101 = REFLECTION OF X(1) IN X(1114) (0.0642, -0.9825) A B C X1 X1114 X30 X40 X165 X1113 X1312 X1698 X1313 X1699 X2101 (a, b, c) = (5, 6, 7) | AB = 1

X2101 (REFLECTION OF X1 IN X1114) 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) is as noted just above X2093
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(24.656992423741\)

X2101 lies on the Bevan circle.

▸ Incident Central Lines5 lines

{1, 1114}, {30, 40}, {165, 1113}, {1312, 1698}, {1313, 1699}

▸ Functional Relations2 relations