## X(265) (REFLECTION OF X(3) IN X(125))

 Interactive Applet

You can move the points A, B and C (click on the point and drag it).
Press the keys “+” and “−” to zoom in or zoom out the visualization window and use the arrow keys to translate it.

You can also construct all centers related with this one (as described in ETC) using the “Run Macro Tool”. To do this, click on the icon , select the center name from the list and, then, click on the vertices A, B and C successively.

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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           sin 2A csc 3A : sin 2B csc 3B : sin 2C csc 3C
= 1/(4 cos A - sec A) : 1/(4 cos B - sec B) : 1/(4 cos C sec C)

Barycentrics    sin A sin 2A csc 3A : sin B sin 2B csc 3B : sin C sin 2C csc 3C

X(265) lies on these lines: 3,125    4,94    5,49    6,13    30,74    64,382    65,79    67,511    69,328    290,316    300,621    301,622

X(265) = reflection of X(I) in X(J) for these (I,J): (3,125), (110,5), (146,1539), (399,113)
X(265) = isogonal conjugate of X(186)
X(265) = isotomic conjugate of X(340)
X(265) = cevapoint of X(5) and X(30)
X(265) = crosspoint of X(94) and X(328)

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