X1161

CIRCUMCENTER OF INNER GREBE TRIANGLE

X1161 is the circumcenter of inner grebe triangle.
< 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) { 1160, 3 }: Brocard Axis { 3, 6 }: Brocard Axis { 4, 1163 }: Central Line L(4, 1163) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_1160 = CIRCUMCENTER OF OUTER GREBE TRIANGLE (0.1258, -0.5160) X_3 = CIRCUMCENTER (0.5000, 0.1021) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_4 = ORTHOCENTER (0.6122, 0.3958) X_1163 = INNER GREBE-ORTHIC PERSPECTOR (0.6431, 0.4339) X_1161 = CIRCUMCENTER OF INNER GREBE TRIANGLE (0.8742, 0.7201) A B C X1160 X3 X6 X4 X1163 X1161 (a, b, c) = (5, 6, 7) | AB = 1

X1161 (CIRCUMCENTER OF INNER GREBE TRIANGLE) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \((1 - 2 \cot A - 2 \cot B - 2 \cot C) \cos A + 2 \sin A : :\)
Search Value (6, 9, 13): \(-28.202458534375\)
▸ Alternate Coordinates1 form

  • Trilinears: \((1 - 2 \cot \omega ) \cos A - 2 \sin A : :\)

▸ Incident Central Lines2 lines

{3, 6}, {4, 1163}

▸ Functional Relations1 relation

Notes

See Hyacinthos #6537.