X1387

MIDPOINT OF INCENTER AND FEUERBACH POINT

X1387 is the midpoint of incenter and Feuerbach point.
< 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, 11 }: Feuerbach Line { 1, 5 }: Feuerbach Line { 7, 104 }: Central Line L(7, 104) { 142, 214 }: Central Line L(142, 214) { 149, 377 }: Central Line L(149, 377) 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_11 = FEUERBACH POINT (0.7347, 0.0667) X_5 = NINE-POINT CENTER (0.5561, 0.2489) X_7 = GERGONNE POINT (0.5903, 0.2769) X_104 = ANTIPODE OF X(100) (0.8571, -0.2624) X_142 = COMPLEMENT OF X(9) (0.5506, 0.2192) X_214 = -CEVA CONJUGATE OF X(44) (0.3571, 0.3499) X_149 = REFLECTION OF X(20) IN X(104) (1.3265, -0.3333) X_377 = EULER LINE INTERCEPT OF LINE X(7)X(8) (0.5473, 0.2258) X_1387 = MIDPOINT OF INCENTER AND FEUERBACH POINT (0.6531, 0.1500) A B C X1 X11 X5 X7 X104 X142 X214 X149 X377 X1387 (a, b, c) = (5, 6, 7) | AB = 1

X1387 (MIDPOINT OF INCENTER AND FEUERBACH POINT) 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 \(f(a,b,c) = bc[2a^{4} - 2(b + c)a^{3} + (8bc - 3b^{2} - 3c^{2})a^{2}\), + 2(b + c)(b - c)2a + (\(b^{2}\) - \(c^{2})\)2]
Barycentrics: \(af(a,b,c) : bf(b,c,a) : cf(c,a,b)\)
Search Value (6, 9, 13): \(2.166721815351\)
▸ Incident Central Lines9 lines

{1, 5}, {2, 1000}, {7, 104}, {30, 1319}, {100, 474}, {106, 1086}, {142, 214}, {149, 377}, {153, 1056}

▸ Functional Relations7 relations