Let
ΔA’B’C’ be a triangle T of a triangle ΔABC. The parallel line to (AB) through B’
cuts (BC) in Ab and the parallel line to (AB) through C’ cuts (BC) in Ac. Build
Ba, Bc, Ca, Cb cyclically. The
perpendicular bisectors of [AbAc], [BaBc] and [Ca,Cb] concur at a point Z(T) for some triangles T.
The
next table shows Z(T) for such triangles.
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TRIANGLE T of ΔABC
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Z(T):
Trilinear center function and properties
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ETC-(6,9,13)-search
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ANTICOMPLEMENTARY
BROCARD1 NAPOLEON INNER NAPOLEON OUTER NEUBERG1 NEUBERG2 VECTEN INNER VECTEN OUTER |
X(3)
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--
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BROCARD2
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a*(18*S^2*SA^2-3*SW*(SW^2+9*S^2)*SA+S^2*(9*S^2-SW^2))
On lines: (2,1495), (353,511), (575,1383) |
8.96309921686445
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COSYMMEDIAN
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a*(18*S^2*SA^2-(54*S^2*R^2+SW*(9*S^2+SW^2))*SA+S^2*(9*S^2-SW^2))
On line: (182,381) |
11.14383553953250
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GREBE INNER
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a*((S-SW)*SA+S^2)
On Brocard Axis (3-6) Midpoint of: (3,1161) On lines: (3,6), (4,487), (25,5409), (30,1991), (51,1584), (325,637), (394,3155), (1306,3563), (1583,3917), (1599,2979), (1600,3060), (3156,5407) |
-10.71004782008930
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GREBE OUTER
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a*((S+SW)*SA-S^2)
On Brocard Axis (3-6) Midpoint of: (3,1160) On lines: (3,6), (4,488), (25,5408), (51,1583), (325,638), (394,3156), (1307,3563), (1584,3917), (1599,3060), (1600,2979), (3155,5406) |
24.27477360848200
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SYMMEDIAL
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a*(2*S^2*SA^2-(SW*(S^2+SW^2)+8*S^2*R^2)*SA+S^2*(S^2-SW^2))
On lines: (3,695), (4,83) |
4.67367749959897
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TANGENTIAL
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a*(2*SA^2-(SW+4*R^2)*SA+S^2)
Midpoint of: (3,1498), (1352,5596) Reflection of: (182/206), (1147/156), (3357/3) On lines: (3,64), (4,54), (5,182), (6,1598), (20,110), (22,5562), (24,185), (25,389), (30,156), (32,1971), (49,382), (52,161), (68,542), (107,1075), (155,159), (186,1204), (221,999), (381,569), (399,2917), (567,3843), (576,2393), (1012,1437), (1216,3098), (1352,3547), (1385,5248), (1397,3073), (1656,1853), (1872,2182), (1899,3542), (1968,3331), (1974,3089), (2175,3072), (2192,3295), (2781,5609), (2818,3556), (3091,5012) |
-5.64011769172535
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