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Q.
Two circle of equal radius $r$ cut orthogonally. If their centres are $(2,3)$ and $(5,6)$ then find value of $r$.
Conic Sections
Solution:
orthogonal intersection
$ r _{1}^{2}+ r _{2}^{2}= d ^{2}$
$ r ^{2}+ r ^{2}=(5-2)^{2}+(6-3)^{2} $
$2 r ^{2}=9+9$
$ r ^{2}=\frac{18}{2}$
$\Rightarrow r ^{2}=9$
$ \Rightarrow r =3$
