Finding the Center and Radius of a circle

In summary, to find the center of a circle, you can use the coordinates of any two points on the circle's circumference. The formula for finding the radius of a circle is r = √(x2 - x1)2 + (y2 - y1)2, where (x1, y1) and (x2, y2) are the coordinates of any two points on the circle's circumference. Yes, you can find the center and radius of a circle with three points by using the circumcenter formula or by measuring the distance from the center to any of the three points. To find the center and radius of a circle using its equation, you can use the standard form of a circle's equation and compare
  • #1
snickersf12
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What is the center and radius of a circle that has a diameter with endpoints (-9,-6) and (-1,0)
 
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  • #2
That's very close to being trivial! The center of the circle is at the midpoint of any diameter. And the midpoint of the line segment between two points is the average of the two points. The center of the circle is the midpoint of the line between (-9, -6) and (-1, 0): ((-9+(-1))/2, (-6+0)/2)= (-10/2, -6/2)= (-5, -3). And the radius is the distance from (-5, -3) to either of the given points.
 

Related to Finding the Center and Radius of a circle

1. How do you find the center of a circle?

To find the center of a circle, you can use the coordinates of any two points on the circle's circumference. The center will be the midpoint of the line segment connecting these two points.

2. What is the formula for finding the radius of a circle?

The formula for finding the radius of a circle is r = √(x2 - x1)2 + (y2 - y1)2, where (x1, y1) and (x2, y2) are the coordinates of any two points on the circle's circumference.

3. Can you find the center and radius of a circle with three points?

Yes, you can find the center and radius of a circle with three points. One method is to use the circumcenter formula, which involves finding the intersection of the perpendicular bisectors of the three line segments formed by the three points. The center of the circle will be the point of intersection, and the radius can be found by measuring the distance from the center to any of the three points.

4. How do you find the center and radius of a circle using its equation?

To find the center and radius of a circle using its equation, you can use the standard form of a circle's equation: (x - h)2 + (y - k)2 = r2, where (h, k) is the center of the circle and r is the radius. By comparing this equation to the given equation of the circle, you can determine the values of h, k, and r.

5. Can you find the center and radius of a circle if only given its circumference?

No, you cannot find the center and radius of a circle with only its circumference. You would also need to know the equation or coordinates of the circle in order to calculate the center and radius. However, if you have the circumference and the area of the circle, you can use the formula C = 2πr and A = πr2 to solve for the radius and then find the center using the methods mentioned in the previous questions.

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