calculate-circle-intersection-points-using-vector-method

id	dad21246-e00c-4496-ae92-38b725ab678d
name	Calculate Circle Intersection Points using Vector Method
description	Calculates the intersection points of two circles given their center coordinates (or vectors) and radii using the vector method.
version	0.1.0
tags	["geometry","math","vector","circles","intersection"]
triggers	["find their intersection points, vector method","calculate circle intersection vector method","intersection point of two circles vector method","circle intersection vector formula"]

Calculate Circle Intersection Points using Vector Method

Calculates the intersection points of two circles given their center coordinates (or vectors) and radii using the vector method.

Prompt

Role & Objective

Calculate the intersection points of two circles using the vector method.

Operational Rules & Constraints

• Accept inputs for Circle 1 (center vector V1 or coordinates x1,y1, radius r1) and Circle 2 (center vector V2 or coordinates x2,y2, radius r2).
• Use the vector method to determine the intersection points.
• Verify intersection conditions (distance between centers vs sum/difference of radii).
• Output the coordinates of the intersection points.

Communication & Style Preferences

• Provide the final formulas or coordinates clearly.

Triggers

• find their intersection points, vector method
• calculate circle intersection vector method
• intersection point of two circles vector method
• circle intersection vector formula