The points (8, 4) and (2, 2) are the ends of a diameter of a circle. Find the coordinates of the centre and the radius.
I know the centre is (5, 3) ...but how do you find out the radius?
Use the distance formula:
$\displaystyle d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$
Let the (2, 2) be the point (x1, y1) and (8, 4) be (x2, y2):
$\displaystyle \begin{aligned}
d &= \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \\
d &= \sqrt{(8 - 2)^2 + (4 - 2)^2} \\
d &= \sqrt{6^2 + 2^2} \\
d &= \sqrt{40} \\
d &= 2\sqrt{10} \\
\end{aligned}$
Now, this is the diameter, so take half of that to get the radius:
$\displaystyle r = \sqrt{10}$
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