Question

If the number of radical axes formed out of a given number of circles be same as the number of radical centres, then find the number of given circles.

Answer 1

Let there be n circles. Radical axis is obtained by taking 2 circles at a time and radical centre is obtained by taking 3 circles at a time
$\therefore$ ${}^n{C}_2{=}^n{C}_3$
$\therefore$ n=$2+3=5$