JEE Main 2020 (Online) 3rd September Morning ShiftQuestion 1
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 ________.
Circle
Answer$3$
Solution
Centre $(a,2-a)$ with $0<a<2$ (first quadrant). Touching $x=3$ and $y=2$: radius $=3-a=|2-(2-a)|=a$. $3-a=a\Rightarrow a=\frac32$, radius $\frac32$, diameter $=3$.