Question

How do you find the center of a circle with the Midpoint formula?

Answer 1

Hint: The center of the circle is nothing but the midpoint of the diameter of the circle. So if we know the end points of the diameter of a circle then we can easily find out the center point of the circle using the midpoint formula given by: $Midpo\mathrm{int}=\left({\displaystyle \frac{x_1+x_2}{2}},{\displaystyle \frac{y_1+y_2}{2}}\right)$.

Complete step by step answer:
Here in this question, they have asked us to find the center of a circle using the midpoint formula. The circle will be as shown in the below diagram.

In the above diagram, $O$ is the center of the circle, and $AB$, $CD$ are the diameters of the circle.
If we know any two endpoints of the diameter of a circle ten we can easily find out the center of the circle by using the midpoint formula.
If we have two endpoints of the diameter of a circle with coordinates $\left(x_1,y_1\right)$ and $\left(x_2,y_2\right)$ the easily we can find the center of the circle by using midpoint formula which is given by:
$Midpo\mathrm{int}=\left({\displaystyle \frac{x_1+x_2}{2}},{\displaystyle \frac{y_1+y_2}{2}}\right)$
Where $x_1,x_2$ are the coordinates of the x-axis.
$y_1,y_2$ are the coordinates of the y-axis.
Simply by substituting the values of coordinates we can solve for the center of a circle.

Note:
Whenever we need to find the center of the circle using the midpoint formula, we need to remember the midpoint formula, if not we don’t get the required answer. We can only find the center using the midpoint formula only if the endpoints of the diameter are known otherwise we cannot find the center of a circle using this method.