How to determine the intersection point of a circle with a certain radius?

Question

Mathematics

Good afternoon, how can you define this?
I have coordinates of point A and B . I also assign the value of the radius r myself. For example, let it be 100. You need to find the coordinates of the point C. Point A coordinates change. X, Y coordinate system.

Answer 1

Given points A (Xa, Ya), B (Xb, Yb), a circle of radius rcentered at the point B. Find the point C (Xc, Yc)lying at the intersection of the ray BAwith the circle
Vector BA = {Xa - Xb, Ya - Yb};
Its length: |BA| = sqrt((Xa - Xb) ^ 2 + (Ya - Yb) ^ 2);
The point Cwill be found if the point is shifted Bby a vector BAdivided by its length and multiplied by r:

Xc = Xb + (Xa - Xb) / |BA| * r,
Yc = Yb + (Ya - Yb) / |BA| * r