Look at the picture.
Use Pythagorean theorem:
[tex]r^2+23^2=(r+10)^2\\\\use\ (a+b)^2=a^2+2ab+b^2\\\\r^2+529=r^2+2\cdot r\cdot10+10^2\\\\r^2+529=r^2+20r+100\ \ \ |subtract\ r^2\ from\ both\ sides\\\\529=20r+100\ \ \ \ |subtract\ 100\ from\ both\ sides\\\\20r=429\ \ \ |divide\ both\ sides\ by\ 20\\\\r=21.45[/tex]
The diameter d = 2r, therefore
[tex]d=2\cdot21.45=42.9[/tex]
