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The radius of an excircle. Let a triangle have exradius r_A (sometimes denoted rho_A), opposite side of length a and angle A, area Delta, and semiperimeter s. Then r_1 = ...

Any one of the eight Apollonius circles of three given circles is tangent to a circle H known as a Hart circle, as are the other three Apollonius circles having (1) like ...

The Hermite constant is defined for dimension n as the value gamma_n=(sup_(f)min_(x_i)f(x_1,x_2,...,x_n))/([discriminant(f)]^(1/n)) (1) (Le Lionnais 1983). In other words, ...

Johnson's theorem states that if three equal circles mutually intersect one another in a single point, then the circle passing through their other three pairwise points of ...

The three circumcircles through the triangle centroid G of a given triangle DeltaA_1A_2A_3 and the pairs of the vertices of the second Brocard triangle are called the McCay ...

Let five circles with concyclic centers be drawn such that each intersects its neighbors in two points, with one of these intersections lying itself on the circle of centers. ...

Draw a circle that cuts three given circles perpendicularly. The solution is known as the radical circle of the given three circles. If it lies outside the three circles, ...

The placement of objects so that they touch in some specified manner, often inside a container with specified properties. For example, one could consider a sphere packing, ...

The circumcircle, Brocard circle, Lemoine axis, and isodynamic points belong to a coaxal system orthogonal to the Apollonius circles, called the Schoute coaxal system. In ...

Draw an initial circle, and arrange six circles tangent to it such that they touch both the original circle and their two neighbors. Then the three lines joining opposite ...