A circle C of radius 2 lies in the second quadrant and touches both the coordinate axes.

Question

A circle C of radius 2 lies in the second quadrant and touches both the coordinate axes. Let r be the radius of a circle that has centre at the point $(2,5)$ and intersects the circle $C$ at exactly two points. If the set of all possible va...

Accepted Answer

${S}_{1}:(x+2{)}^{2}+(y-2{)}^{2}={2}^{2}$

${S}_{2}:(x-2{)}^{2}+(y-5{)}^{2}={r}^{2}$

Both circle intersect at two points

$\begin{gathered} 	herefore |{r}_{1}-{r}_{2}|<{c}_{c}{c}_{2}<{r}_{1}+{r}_{2} \ |r-2|<5<2+r \ \Rightarrow 3<r<7 \ r\in (3,7) \ \alpha =3,\beta =7 \ 3\beta -2\alpha =15 \end{gathered}$

Solutions · 1