First slide

Analysis of two circles in circles

Question

Let there be $n (\geq 3)$ circles. The value of n for which the number of radical axis of these circles is same as the number of radical centres, is

Moderate

A

3
B

4
C

5
D

8

Solution

Since a radical axis is generated by two circles and a radical centre is obtained from three circles. Therefore, Number of radical axes $=^{n} C_{2},$
Number of radical centres $=^{n} C_{3},$
It is given that $^{n} C_{2} =^{n} C_{3} \Rightarrow n = 5$ .

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