How to calculate the radius of the curved side of a triangle?

In this image, only having these dimensions, is it possible to calculate the radius of the circle (of the arc of the line AB)?

The centre of the circle is in the same X position as the line AC, but its Y position is unknown,

How can I do it? Sorry if it's a duplicate question, I could not find how to do this,

If $X$ is the centre of the circle, and $r$ is its radius, then by Pythagoras in triangle $BCX$, $BX^2=r^2=(r-3)^2+4^2$.

So you just have to solve the equation $$r^2=(r-3)^2+16$$

Here is another way to calculate the radius. The construction is the same as Ethan's. In the figure below, $OM$ is the perpendicular bisector of $AB$, and $OA$ is the desired radius.

To find the length of $OA$, note that $\triangle AOM$ is similar to $\triangle ABC$, which is the famous 3-4-5 triangle. Now, $AM = \frac52$ , so $OA = $ ?

Construct the perpendicular bisector $L$ of segment $AB$. The point at which $L$ meets the line containing $AC$ is the center of the circle you want.