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The orthocubic (or ortho cubic) Z(X_4) is a self-isogonal cubic with pivot point at the orthocenter H, so it has parameter x=cosBcosC and trilinear equation (Cundy and Parry ...

Two triangles DeltaA_1B_1C_1 and DeltaA_2B_2C_2 are orthologic if the perpendiculars from the vertices A_1, B_1, C_1 on the sides B_2C_2, A_2C_2, and A_2B_2 are concurrent. ...

Given a pair of orthologic triangles, the point where the perpendiculars from the vertices of the first to the sides of the second concur and the point where the ...

The orthoptic circle of the Steiner inellipse is the circle with center at alpha_2=1/a, (1) corresponding to the triangle centroid G and radius ...

Consider a reference triangle DeltaABC and any given point P. The perpendiculars to AP, BP and CP respectively meet BC, AC and AB in three collinear points defining line l. ...

A similar construction can be done by initially erecting a square internally on the side BC. This leads to the A^--inscribed square. The triangle DeltaX^-Y^-Z^- of centers of ...

The outer Vecten circle is the circumcircle of the outer Vecten triangle. It has center at Kimberling center X_(641), which is the complement of the outer Vecten point ...

A papal cross is a cross having three crossbars. A schematic polyomino version of a papal cross is illustrated above.

For a parabola oriented vertically and opening upwards, the vertex is the point where the curve reaches a minimum.

Mark a point P on a side of a triangle and draw the perpendiculars from the point to the two other sides. The line between the feet of these two perpendiculars is called the ...