A circle intersects the coordinate axes at points $A(a, 0), B(b, 0) C(0, c)$ and $D(0, d)$. Find the coordinates of its center.
The center $O(x, y)$ of the given circle is the intersection of the perpendicular bisectors of the chords $A B$ and $C D$. The equations of these perpendiculars are:

$x=1 / 2(a+b)$ and $y=1 / 2(c+d)$ respectively.

## Answer

$\left(\frac{a+b}{2} ; \frac{c+d}{2}\right)$