Circle defined by 3 points calculator
![Print circle defined by 3 points calculator Print circle 3 points](/Images/Buttons/print3.png)
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Equation of a circle passing through 3 points (x1, y1) (x2, y2) and (x3, y3) summary
![Print 3 points circle summary](/Images/Buttons/print3.png)
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The coefficients A, B, C and D can be found by solving the following determinants: ![]() ![]() ![]() ![]() ![]() |
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Center point (x, y) and the radius of a circle passing through 3 points (x1, y1) (x2, y2) and (x3, y3) are: ![]() |
Example 1 - Circle Defined by 3 Points
![Print Example 1 - Circle defined by 3 points Ex-1](/Images/Buttons/print3.png)
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Find the equation of a circle that passes through the points (⎯3 , 4) , (4 , 5) and (1 , ⎯4).
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Example 2 - Circle Defined by 3 Points
![Print example 2 - Circle defined by 3 points Ex-2](/Images/Buttons/print3.png)
Find the equation of a circle and its center and radius if the circle passes through the points (3 , 2) ,
(6 , 3) and (0 , 3). |
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After dividing all terms by 6 we get: A = 1 B =−6 C = −14 D = 33.
And the equation of the circle is: x2 + y2 ⎯ 6x ⎯ 14y + 33 = 0 In order to find the radius of the circle use the general circle equation and perform some basic algebraic steps and with the help of the square form (a + b)2 = a2 + 2ab + b2 we get
The last equation is a circle with the center and radius equals to (notice the minus sign at x and y):
The equation of the circle can be presented by the center and the radius as: (x ⎯ 3)2 + (y ⎯ 7)2 = 52
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