Question

The radius of the circle passing through the points $(1,2)(5,2)$ and $(5,-2)$ is :

• A. $5\sqrt{2}$
• B. $2\sqrt{5}$
• C. $3\sqrt{2}$
• D. $2\sqrt{2}$

Answer 1

The correct option is D $2\sqrt{2}$

From symmetry of the points( these coordinates make 3 corners of square )that the center will be at the point (3,0).

Taking distance between points (3,0) and (5,2)

Using Pythagoras theorem

Radius, $r^2=(5-3{)}^2+(2-0{)}^2$

$r^2=2^2+2^2$

$r=\sqrt{4+4}$

$r=\sqrt{8}$

$r=2\sqrt{2}$