10.1 circle and system of circle — ગણિત ધોરણ 11 સાયન્સ — Question

$\left(x-\frac{a}{2}\right)^{2}+y^{2}=\frac{a^{2}}{4}, \quad x^{2}+y^{2}=c^{2}$

Centre $\left(\frac{a}{2}, 0\right)$ and $(0,0)$ and radius $=\frac{a}{2}$ and $c$

$\sqrt{\left(\frac{a}{2}\right)^{2}+(0-0)}=|| \frac{a}{2}|\pm c|$ 

$ \Rightarrow\left|\frac{a}{2}\right|=|| \frac{a}{2}|\pm c|$

$\Rightarrow\left|\frac{a}{2}\right|=c-\left|\frac{a}{2}\right|, \quad \therefore|a|=c$