Question

Let there be $n\ge 3$ circles in a plane. The value of n for which the number of radical centers is equal to the number of radical axes is (assume that all radical axes and radical centers 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. Then total number of radical centres is ${}^n{C}_3$.
And for a radical axis two circles are required. Then total number of radical axis is ${}^n{C}_2$.
Now given , ${}^n{C}_2{=}^n{C}_3\Rightarrow n=5$