Finding center and radius of a circle

Hello Everyone,

I came across a simple topic which I cannot understand in my Precalculus class.

It is an algebra topic which needs me to find the circle.

it gives me two points. (1,2) and (4,2)
I would say the solution is to find the distance within the 2 points and half is the radius. Which is 3/2
Now how exactly can I find the center?

There is an infinite number of circles passing through two given points.

If you are given that (1, 2) and (4, 2) is a diameter, then the center is at ((1+4)/2, (2+ 2)/2)= (5/2, 2) and the radius is 3/2 as you say.
But all you are given is two points (and, in fact, you did not say they were points on the circle, then there are an infinite number of such circles, as emakarov said. Or it might be that you were given that (1, 2) is the center and (4, 2) on the circle or vice-versa. Please tell us exactly what the problem says! Just saying you were given two points and "find the circle" doesn't make any sense.

Quote:

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Originally Posted by emakarov

There is an infinite number of circles passing through two given points.

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Quote:

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Originally Posted by HallsofIvy

If you are given that (1, 2) and (4, 2) is a diameter, then the center is at ((1+4)/2, (2+ 2)/2)= (5/2, 2) and the radius is 3/2 as you say.
But all you are given is two points (and, in fact, you did not say they were points on the circle, then there are an infinite number of such circles, as emakarov said. Or it might be that you were given that (1, 2) is the center and (4, 2) on the circle or vice-versa. Please tell us exactly what the problem says! Just saying you were given two points and "find the circle" doesn't make any sense.

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Yeah, I definitely said something which doesn't make sense. I meant to say these two points are on the circle how could I find the center.
I see that you answered that question.