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