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Two figures are homothetic if they are related by an expansion or geometric contraction. This means that they lie in the same plane and corresponding sides are parallel; such ...

Steiner gave and Droz-Farny (1901) proved that if equal circles are drawn about the vertices of a triangle (dashed circles in the above figure), they cut the lines joining ...

The radical circle of three given circles is the circle having center at the radical center of the three circles and is orthogonal to all of them. (A circle with center at ...

The center of any sphere which has a contact of (at least) first-order with a curve C at a point P lies in the normal plane to C at P. The center of any sphere which has a ...

The circumcircle is a triangle's circumscribed circle, i.e., the unique circle that passes through each of the triangle's three vertices. The center O of the circumcircle is ...

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 ...

The inconic having inconic parameters x:y:z=a/(b+c-a):b/(a+c-b):c/(a+b-c). Its center is the mittenpunkt M of the triangle and its Brianchon point is the Nagel point Na. The ...

Consider the circles centered on the midpoints of the sides of a reference triangle and passing though the orthocenter H. These circles cut the sides in six points lying on a ...

The symmedial triangle DeltaK_AK_BK_C (a term coined here for the first time), is the triangle whose vertices are the intersection points of the symmedians with the reference ...

Given a circle, the apothem is the perpendicular distance r from the midpoint of a chord to the circle's center. It is also equal to the radius R minus the sagitta h, r=R-h. ...