# Calculate the closest point to the center of a circle from another circle on its radius.

There are 2 circles, the smaller one has its center on the bigger circles border, from that how can you calculate the coordinates the closest point on the smaller circle to the center of the bigger one. I want to find the coordinates of the closest point of the circle given that I have the height and width and radius of both circles and the position of both circles.

• Connect the two centers with a line, then intersect that line with the small circle. Jul 14, 2014 at 18:48
• @vadim123 maybe the question wasn't clear enough, I edited it, I want to find the position of the point in a coordinate system.
– Nick
Jul 14, 2014 at 18:52
• You can follow my method algebraically. Which step do you have trouble with? Jul 14, 2014 at 18:54

If you know the radius of both circles, then the distance from the center of the larger circle to the closest point on the smaller circle is $r_1-r_2$, where $r_1$ is the radius of the larger circle and $r_2$ is the radius of the smaller. If, as it appears, the center of the smaller circle is also on the $x$-axis, then you have your answer, once you make it negative and plug it into an ordered pair. If not, then you need to use the trigonometric functions to find the coordinates of the center, and then solve for the coordinates of a point $r_1-r_2$ in the direction of the angle.