# Equation to determine radius for a circle that should intersect a given point?

Simple question. I tried Google but I don't know what search keywords to use.

I have two points on a 2d plane. Point 1 = x1 and y1, and Point 2 = x2 and y2.

I'd like to draw a circle around Point 1, and the radius of the circle should be so that it intersects exactly with Point 2.

What is the equation to determine the required radius?

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## 3 Answers

Let's call the center of the circle: $P_1 = (x_1, y_1).\;$

Let $P_2 = (x_2, y_2)$ be a point on circle. Then:

$r$: radius of the circle = distance between points $P_1$ and $P_2$, where

$$r = \sqrt{(x_2 - x_1)^2 + (y_2-y_1)^2}$$

Any point $(x_i, y_i)$ satisfying the equation $(x_i - x_1)^2 + (y_i - y_1)^2 = r^2$ also lies on this circle.

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The radius is simply the distance between the two points. So use the standard Euclidean distance which you should have learned.

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If $P_1(x_1,y_1)$ is the center, the radius will be $\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

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