Question

If the endpoints of a diameter of a circle are (6,2) and (0, 2); what is the radius of
the circle?

Answer 1

Answer:

The radius of circle is 3

Step-by-step explanation:

Given the endpoints of diameter of a circle are (6,2) and (0,2)

We know that the equation of circle is

$(x-h)^{2}$+$(y-k)^{2}$ = $r^{2}$

where (x,y) is any point on the circle, (h,k) is center of the circle and r is radius of circle.

To find (h,k): the center is midpoint of diameter

Midpoint of diameter with end points (x1,y1) and (x2,y2) is given by

( $\frac{x1+x2}{2}$ ,$\frac{y1+y2}{2}$ )

( $\frac{6+0}{2}$ , $\frac{2+2}{2}$ )

(3, 2)

Hence (h,k) is (3,2)

Substituting values of (h.k) and (x.y) as (3,2) and (0,2) respectively, we get

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

$r^{2}$ = $3^{2}$

r =3

Hence the radius of the circle is 3