X3222

ISOGONAL CONJUGATE OF X3221

X3222 is the isogonal conjugate of X3221.
< 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) { 2, 699 }: Central Line L(2, 699) { 645, 803 }: Central Line L(645, 803) { 799, 932 }: Central Line L(799, 932) { 729, 1078 }: Central Line L(729, 1078) { 733, 1799 }: Central Line L(733, 1799) { 111, 2998 }: Central Line L(111, 2998) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_2 = CENTROID (0.5374, 0.2000) X_669 = CROSSDIFFERENCE OF X(2) AND X(39) (-4.3514, 4.6163) X_699 = EVEN (- 4, - 2) CIRCUMCIRCLE POINT (0.9822, 0.2692) X_645 = BARYCENTRIC MULTIPLIER FOR KIEPERT PARABOLA (-0.0375, 0.2992) X_803 = o-(- 2, 1) CIRCUMCIRCLE POINT (0.0155, -0.0581) X_799 = ISOGONAL CONJUGATE OF X(798) (0.0470, 0.3636) X_932 = -CROSS CONJUGATE OF X(100) (0.0354, 0.3132) X_729 = EVEN (- 2, 0) CIRCUMCIRCLE POINT (1.0096, 0.1290) X_1078 = INTERSECTION OF LINES X(2)X(32) AND X(3)X(76) (0.4771, 0.1215) X_733 = EVEN (- 2, 2) CIRCUMCIRCLE POINT (1.0071, 0.0450) X_1799 = INVERSE MIMOSA TRANSFORM OF X(75) (0.4477, 0.0833) X_111 = PARRY POINT (0.9885, -0.0457) X_2998 = CD(X(32)) (0.2505, 0.0728) X_3222 = ISOGONAL CONJUGATE OF X(3221) (-0.0102, 0.1147) A B C X2 X669 X699 X645 X803 X799 X932 X729 X1078 X733 X1799 X111 X2998 X3222 (a, b, c) = (5, 6, 7) | AB = 1

X3222 (ISOGONAL CONJUGATE OF X3221) 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 \(f(a,b,c) = 1/[a(b^{2} - c^{2})(c^{2}a^{2} + a^{2}b^{2} - b^{2}c^{2})]\)
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(10.504559765824\)

X3222 lies on the circumcircle.

▸ Incident Central Lines6 lines

{2, 699}, {111, 2998}, {645, 803}, {729, 1078}, {733, 1799}, {799, 932}

▸ Functional Relations6 relations