How to find the smallest distance between two circles. We assume that the total cost don't overlap, That means they don't interact.

So here, the question that we need to make is that we have to solve this equation, We're going to use the distance formula to find the resets between the two. So the distance between the sources is lying on the line. Connecting the Diameters, or the centers of the circles. So we have the, the coordinates of the centers of the circles. We can construct a line. And that line, we can see that that line intersect the the circles in Different points. So we have the coordinates of the pawns and therefore we can find the smaller distance so we can see that the distance between the two centers is equal to the radii of the forces, alcohol plus that of the second Circle plus the distance between the two circles we can solve for that distance and find our formula Later. We're going to use calculus to find the smallest distance between the total cost. We're gonna use derivatives and limits and find in using firmware theorem to find the Smallest distance. Between the two. We're going to accept this Distance formula for now and we're going to apply it in a concrete example. So we have two circles that are centered at two different points and having two different idea eyes and we want to find

The distance between the two and after that, we can finish our work. So the key idea here is that we now have to find the distance between two circles. All we need to do is to apply that formula using the distance formula that we have seen before. These problem can be beneficial to students go into Oxford exam and to students doing MIT Stanford Princeton Or Berkeley math. Competitions. It is also useful for students, doing AP calculus, and to student doing all ampere and to teachers trying to get their math licensure or to teachers trying to get their practice math 5161.