Draw the 30 cm line.

Bisect it, the circle centre lies on this bisector.

draw a parallel line 23 cm away.

Locate where the bisector cuts that line.

Draw the 16 cm line by going 8 cm away from the intersection

of this line and the bisector of the 30 cm line.

Now take the two extreme points near each other at the end of both lines.

Join these points and bisect the line.

The intersection of the 2 bisectors is the circle centre

because you have found a point equidistant from all 4 endpoints.