Question

Let there be $n\ge 3$ circles in a plane. The value of $n$ for which the number of radical centres is equal to the number of radical axes is (assume that all radical axes and radical centre exist and are different)

• A. $7$
• B. $6$
• C. $5$
• D. None of these

Answer 1

The correct option is C $5$

For a radical centre, $3$ circles are required. The total number of radical centres is ${}^n{C}_3$. The total number of radical axis is ${}^n{C}_2$.
Now,
${}^n{C}_2{=}^n{C}_3\Rightarrow n=5$.