X(27) (CEVAPOINT OF ORTHOCENTER AND CLAWSON CENTER)

 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.

 The JRE (Java Runtime Environment) is not enabled in your browser!

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

 Information from Kimberling's Encyclopedia of Triangle Centers

Trilinears           (sec A)/(b + c) : (sec B)/(c + a) : (sec C)/(a + b)
Barycentrics    (tan A)/(b + c) : (tan B)/(c + a) : (tan C)/(a + b)

X(27) lies on these lines:
2,3    6,1246    7,81    19,63    57,273    58,270    84,1896    86,1474    103,107    110,917    226,284    239,1829    243,1859    295,335    306,1043    393,967    579,1751    648,903    662,913    1014,1440    1088,1434    1268,1796    1719,1733    1730,1746    1770,1780

X(27) is the {X(2),X(4)}-harmonic conjugate of X(469).

X(27) = isogonal conjugate of X(71)
X(27) = isotomic conjugate of X(306)
X(27) = inverse-in-orthocentroidal-circle of X(469)
X(27) = complement of X(3151)
X(27) = anticomplement of X(440)
X(27) = X(286)-Ceva conjugate of X(29)
X(27) = cevapoint of X(I) and X(J) for these (I,J): (4,19), (57,278)
X(27) = X(I)-cross conjugate of X(J) for these (I,J): (4,286), (19,28), (57,81), (58,86)
X(27) = crossdifference of any two points on line X(647)X(810)
X(27) = X(I)-Hirst inverse of X(J) for these (I,J): (2,447), (4,423)
X(27) = X(I)-beth conjugate of X(J) for these (I,J): (648,27), (923,27)

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