The diameter of the circle, whose centre lies on the line x+y=2 in the first quadrant and …

Question

The diameter of the circle, whose centre lies on the line $x+y=2$ in the first quadrant and which touches both the lines $x=3$ and $y=2$, is \_\_\_\_\_\_\_\_.

Answer: 3

Accepted Answer

Centre $(a,2-a)$. Distance to $x=3$: $|a-3|$; distance to $y=2$: $|{-a}|=a$ (first quadrant).

$$|a-3|=a\Rightarrow a=\frac32\ (\text{for }a<3),\qquad r=\frac32.$$

$$\text{Diameter}=3.$$

Solutions · 1