## X(1123) (PAASCHE POINT)

 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/(1 + sin A) : 1/(1 + sin B) : 1/(1 + sin C)
Barycentrics    (sin A)/(1 + sin A) : (sin B)/(1 + sin B) : (sin C)/(1 + sin C)

Let D and E be the congruent circles each tangent to the other and to line BC, with D also tangent to line AB and E also tangent to one CA, meeting in a point A' lying outside triangle ABC. Define B' and C' cyclically. Then A'B'C' is perspective to ABC, and the perspector is X(1123). See

Ivan Paasche, Aufgabe P 933, Praxis der Mathematik 1 (1990), page 40.

X(1123) lies on these lines: 2,586    37,158    57,482

X(1123) = isogonal conjugate of X(1124)
X(1123) = isotomic conjugate of X(1267)

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