# The diameter of the circle, whose centre lies on the line x+y=2 in the first qaudrant and which touches both the lines x=3 and y=2, is_____ Option: 1 1 Option: 2 2 Option: 3 3 Option: 4 4

The center of the circle = (k,2-k) circle is pass via point (0,2) and (3,0)

$\frac{k-3}{\sqrt{1^{2}+0^{2}}}=\left | \frac{2-k-2}{\sqrt{1^{2}+0^{2}}} \right |$

$\left | k-3 \right |=\left | k \right |$

$\left | k-3 \right |=\pm k$

$k=\frac{3}{2}$

centre =$\left (\frac{3}{2} , \frac{1}{2} \right )$

diameter (x) = $2\times \left | k-3 \right |=2 \times \left | \frac{3}{2}-3 \right |=2\times \frac{3}{2}=3 unit$

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