Question

If the radius of one circle is twice the radius of another circle whose centres are $(2,0)$ and $(1,2)$ respectively are cutting orthogonally, then the radius of the second circle is

• A. $1$
• B. $2$
• C. $3$
• D. $5$

Answer 1

The correct option is B $2$

If angle between circle is ${90}^0,$ then circles are cutting orthogonally
In $\Delta A{C}_1{C}_2$, applying pythagoras theorem
$\therefore r_1^2+r_2^2=(C_1{C}_2{)}^2$
Given,

$r_2=2r_1$

$\Rightarrow r_1^2+(2r_1{)}^2=(\sqrt{5}{)}^2$
$\Rightarrow 5r{{}_1}^2=5$
$\Rightarrow r_1=1$
$\therefore r_2=2$

Hence, option B.