SOLUTION: Show that the points (-2,5),(-2,-1) and (4,-1) all lie on a circle whose center is at (1,2). Find the length of the radius.

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Question 166148: Show that the points (-2,5),(-2,-1) and (4,-1) all lie on a circle whose center is at (1,2). Find the length of the radius.
Answer by Mathtut(3670) About Me  (Show Source):
You can put this solution on YOUR website!
since C(1,2) is the center if all lie on the circle then the distance between each point and C should be equal and would be the length of the radius.
distance between 2 points is sqrt%28%28change-in-x%29%5E2%2B%28change-in-y%29%5E2%29
so distance between the following points and C are:
(-2,5) sqrt%28%28-2-1%29%5E2%2B%285-2%29%5E2%29---->sqrt%28-3%5E2%2B3%5E2%29=3sqrt%282%29
(-2,-1) sqrt%28%28-2-1%29%5E2%2B%28-1-2%29%5E2%29--->sqrt%28-3%5E2%2B-3%5E2%29=3sqrt%282%29
(4,-1) sqrt%28%284-1%29%5E2%2B%28-1-2%29%5E2%29---->sqrt%283%5E2%2B-3%5E2%29=3sqrt%282%29
they all lie on the circle with a radius of 3sqrt%282%29