Let us assume that the coordinates of the center of the circle are C(h,k) and its radius is r.
Now, since the circle touches X-axis at (1,0), hence its radius should be equal to ordinate of center.
\(\implies\) r = k
Hence, the equation of circle is \((x – h)^2 + (y – k)^2\) = \(k^2\)
Also, given that the circle passes through points (1, 0) and (2, 3). Hence, substituting them, in the equation of circle we get
\((1 – h)^2 + (0 – k)^2\) = \(k^2\) ……(i)
\((2 – h)^2 + (3 – k)^2\) = \(k^2\) ……(ii)
from equations (i) and (ii), we get
k = \(5\over 3\)
Hence, The diameter of the circle is 2k = \(10\over 3\)
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