## X(33) (PERSPECTOR OF THE ORTHIC AND INTANGENTS TRIANGLES)

 Interactive Applet

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This applet was built with the free and multiplatform dynamic geometry software C.a.R..

 Information from Kimberling's Encyclopedia of Triangle Centers

Trilinears           1 + sec A : 1 + sec B : 1 + sec C = tan A cot(A/2) : tan B cot(B/2) : tan C cot(C/2)
= f(a,b,c) : f(b,c,a) : f(c,a,b), where f(a,b,c) = (b + c - a)/(b2 + c2 - a2)
= g(A,B,C) : g(B,C,A) : g(C,A,B), where g(A,B,C) = sec A cos2(A/2)

Barycentrics    sin A + tan A : sin B + tan B : sin C + tan C
= h(A,B,C) : h(B,C,A) : h(C,A,B), where h(A,B,C) = tan A cos2(A/2)

X(33) lies on these lines:
1,4    2,1040    5,1062    6,204    7,1041    8,1039    9,212    10,406    11,427    12,235    19,25    20,1038    24,35    28,975    29,78    30,1060    36,378    40,201    42,393    47,90    56,963    57,103    63,1013    64,65    79,1063    80,1061    84,603    112,609    200,281    210,220    222,971    264,350

X(33) is the {X(1),X(4)}-harmonic conjugate of X(34).

X(33) = isogonal conjugate of X(77)
X(33) = X(I)-Ceva conjugate of X(J) for these (I,J): (4,19), (29,281), (318,9)
X(33) = X(I)-cross conjugate of X(J) for these (I,J): (41,9), (42,55)
X(33) = crosspoint of X(I) and X(J) for these (I,J): (1,282), (4,281)
X(33) = crosssum of X(I) and X(J) for these (I,J): (1,223), (3,222), (57,1394), (73,1214)
X(33) = crossdifference of any two points on line X(652)X(905)
X(33) = X(33)-beth conjugate of X(25)

This is a joint work of
Humberto José Bortolossi, Lis Ingrid Roque Lopes Custódio and Suely Machado Meireles Dias.