...finding the radius

**Joker37** · June 20th 2009, 04:37 AM

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?

**yeongil** · June 20th 2009, 04:52 AM

Originally Posted by Joker37

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:
$d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$

Let the (2, 2) be the point (x1, y1) and (8, 4) be (x2, y2):

$\begin{aligned} d &= \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \\ d &= \sqrt{(8 - 2)^2 + (4 - 2)^2} \\ d &= \sqrt{6^2 + 2^2} \\ d &= \sqrt{40} \\ d &= 2\sqrt{10} \\ \end{aligned}$

Now, this is the diameter, so take half of that to get the radius:
$r = \sqrt{10}$

01

**Joker37** · June 20th 2009, 05:12 AM

Originally Posted by yeongil

Use the distance formula:
$d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$

Forgot about the distance formula.

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