Add to ORKGWe study some properties of a triad of circles associated with a triangle. Each circle is inside the triangle, tangent to two sides of the triangle, and externally tangent to the circle on the third side as diameter. In particular, we find a nice relation involving the radii of the inner and outer Apollonius circles of the three circles in the triad.Comment: arXiv admin note: text overlap with arXiv:2310.1289
Dr. Ron Knott constructed a graph of all Primitive Pythagorean Triples (PPTs) with legs up to length...
Inverting the vertices of elliptic billiard N-periodics with respect to a circle centered on one foc...
summary:In the first part, we assume well known characteristics of ellipse which are given by triang...
We study properties of certain circles associated with a triangle. Each circle is inside the triangl...
We revisit constructions based on triads of conics with foci at pairs of vertices of a reference tri...
In this article, we introduce an algorithm for automatic generation and categorization of triangle g...
Abstract. We give a simple construction of the Apollonius circle without di-rectly invoking the exci...
Given a triangle ABC there is a similar triangle AB′C ′ such that B′C ′ is the side of an inscribed ...
In Tangencies Apollonius of Perga showed how to construct a circle that is tangent to three given ci...
Abstract. We derive the general equation for the radius of the inner tangent circle that is associat...
In this article we’ll present the properties of the radicale axes and the adjoin circles of a triang...
Any triangle ABC have three symmedian lines that intersect at one point K that called symmedian poin...
Abstract. The three Apollonius circles of a triangle, each passing through a triangle vertex, the co...
The triangles formed by the triples in Pythagoras’ or Plato’s families can be geometrically intercon...
Abstract: Circles through the Brocard points (Omega circles) share nearly all the properties of cir...
Dr. Ron Knott constructed a graph of all Primitive Pythagorean Triples (PPTs) with legs up to length...
Inverting the vertices of elliptic billiard N-periodics with respect to a circle centered on one foc...
summary:In the first part, we assume well known characteristics of ellipse which are given by triang...
We study properties of certain circles associated with a triangle. Each circle is inside the triangl...
We revisit constructions based on triads of conics with foci at pairs of vertices of a reference tri...
In this article, we introduce an algorithm for automatic generation and categorization of triangle g...
Abstract. We give a simple construction of the Apollonius circle without di-rectly invoking the exci...
Given a triangle ABC there is a similar triangle AB′C ′ such that B′C ′ is the side of an inscribed ...
In Tangencies Apollonius of Perga showed how to construct a circle that is tangent to three given ci...
Abstract. We derive the general equation for the radius of the inner tangent circle that is associat...
In this article we’ll present the properties of the radicale axes and the adjoin circles of a triang...
Any triangle ABC have three symmedian lines that intersect at one point K that called symmedian poin...
Abstract. The three Apollonius circles of a triangle, each passing through a triangle vertex, the co...
The triangles formed by the triples in Pythagoras’ or Plato’s families can be geometrically intercon...
Abstract: Circles through the Brocard points (Omega circles) share nearly all the properties of cir...
Dr. Ron Knott constructed a graph of all Primitive Pythagorean Triples (PPTs) with legs up to length...
Inverting the vertices of elliptic billiard N-periodics with respect to a circle centered on one foc...
summary:In the first part, we assume well known characteristics of ellipse which are given by triang...