X995

MIDPOINT OF X1 AND X43

X995 is the midpoint of X1 and X43.
< 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, 43 }: Nagel Line { 1, 2 }: Nagel Line { 31, 36 }: Central Line L(31, 36) { 6, 101 }: Central Line L(6, 101) { 56, 58 }: Central Line L(56, 58) 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_43 = -CEVA CONJUGATE OF X(1) (0.6358, 0.2963) X_2 = CENTROID (0.5374, 0.2000) X_31 = 2nd POWER POINT (0.6228, 0.3008) X_36 = INVERSE-IN-CIRCUMCIRCLE OF INCENTER (1.3333, 1.6330) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_101 = Ψ(INCENTER, SYMMEDIAN POINT) (0.2143, 0.5249) X_56 = EXSIMILICENTER(CIRCUMCIRCLE, INCIRCLE) (0.6316, 0.3438) X_58 = ISOGONAL CONJUGATE OF X(10) (0.6107, 0.2850) X_995 = MIDPOINT OF X(1) AND X(43) (0.6036, 0.2648) A B C X1 X43 X2 X31 X36 X6 X101 X56 X58 X995 (a, b, c) = (5, 6, 7) | AB = 1

X995 (MIDPOINT OF X1 AND X43) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(a(ab + ac - bc + b^{2} + c^{2}) : :\)
Search Value (6, 9, 13): \(0.973764684796\)
▸ Incident Central Lines11 lines

{1, 2}, {3, 595}, {6, 101}, {31, 36}, {56, 58}, {57, 957}, {238, 993}, {581, 1104}, {609, 1055}, {758, 982}, {991, 1064}

▸ Functional Relations4 relations

Notes

See Dasari Naga Vijay Krishna, On a Conic Through Twelve Notable Points, Int. J. Adv. Math. and Mech. 7(2) (2019) 1-15.