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Let t, u, and v be the lengths of the tangents to a circle C from the vertices of a triangle with sides of lengths a, b, and c. Then the condition that C is tangent to the ...

The catacaustic of the quadrifolium with arbitrary radiant point is a complicated function. A few example are illustrated above.

The Scarabaeus curve is a sextic curve given by the equation (x^2+y^2)(x^2+y^2+ax)^2-b^2(x^2-y^2)^2=0 and by the polar equation r=bcos(2theta)-acostheta where a,b!=0.

If a triangle is inscribed in a conic section, any line conjugate to one side meets the other two sides in conjugate points.

External (or positive) and internal (or negative) similarity points of two circles with centers C and C^' and radii r and r^' are the points E and I on the lines CC^' such ...

The external (internal) similarity point of two fixed circles is the point at which all the circles homogeneously (nonhomogeneously) tangent to the fixed circles have the ...

The triquetra is a geometric figure consisting of three mutually intersecting vesica piscis lens shapes, as illustrated above. The central region common to all three lenses ...

The conchoid of de Sluze is the cubic curve first constructed by René de Sluze in 1662. It is given by the implicit equation (x-1)(x^2+y^2)=ax^2, (1) or the polar equation ...

An oval dissected into pieces which are to used to create pictures. The resulting figures resemble those constructed out of tangrams.

The cyclocevian triangle DeltaA^('')B^('')C^('') of a reference triangle DeltaABC with respect to a point P is the triangle formed by the vertices determined by the ...