Question

If the circles of equal radius and centers at $(2,3),(5,6)$ cut orthogonally, then the radius of one of the circles is

• A. $3$
• B. $3\sqrt{2}$
• C. $6$
• D. $4$

Answer 1

The correct option is A $3$

If two circles are orthogonal to each other then,
$r{{}_1}^2+r{{}_2}^2=(c_1{c}_2{)}^2$
Given $r_1=r_2=r$ and $c_1=(2,3)$ and $c_2=(5,6)$
So, $2r^2=(3\sqrt{2}{)}^2$
$r=3$