Circles

Tangent to x-axis means center is at $(h, r)$. Perpendicular bisector of chord from $(0,4)$ to $(6,4)$ is $x = 3$, so $h=3$. Then $(3-0)^2 + (r-4)^2 = r^2$, so $9 + r^2 - 8r + 16 = r^2$, giving $8r = 25$, $r = \\frac{25}{8}$. Hmm, recompute: $9 - 8r + 16 = 0$, so $8r = 25$, $r = \\frac{25}{8}$. None match exactly... The answer should be $\\frac{25}{8}$, but the closest option is $\\frac{13}{2}$ if the points were different. Re-reading: $r = \\frac{25}{8}$ doesn't match. Let me revise: with points $(0,4)$ and $(6,4)$, $r = 25/8 = 3.125$.