# Circle-Cirle Intersection

Sorry for asking a question like this (can't comment as my reputation is too low). Could someone please explain this answer to me? Particularly the part, where the orthogonal vectors are declared? Why are the vectors declared as such? What is the reasoning or math behind declaring them in such a way?

Given the points $(x_1,y_1)$ and $(x_2,y_2)$. We focus on the center point of both circles given by $$\left( \frac{x_1+x_2}{2}, \frac{y_1+y_2}{2} \right).$$

The distance between the centers of the circles is given by $$R = \sqrt{ (x_2-x_2)^2 + (y_2-y_1)^2}.$$

We can consider the following orthogonal vectors $$\vec{a} = \left( \frac{x_2-x_1}{R}, \frac{y_2-y_1}{R} \right), \vec{b} = \left( \frac{y_2-y_1}{R}, - \frac{x_2-x_1}{R} \right).$$

• I've posted a comment there for you. – iamvegan Aug 21 '16 at 20:13
• Your orthogonal vectors $a$ and $b$ are not right. One of the components of $b$ needs to be multiplied by $(-1)$. – Futurologist Aug 21 '16 at 23:34