I have this question. I get from the user coordinates of 3 points (x, y). These three points are vertices of a triangle. My task is to find the center of the circumscribed circle, that is, the coordinates of the center. Who has ideas how to do it.

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    intersection of perpendiculars to two sides of a triangle, drawn through the midpoints of these sides (where does the assembler?) - Igor

1 answer 1

The center of the circumscribed circle is defined by the formulas

| x_a^2 + y_a^2 y_a 1 | x = | x_b^2 + y_b^2 y_b 1 | * 1/d | x_c^2 + y_c^2 y_c 1 | | x_a^2 + y_a^2 x_a 1 | y = | x_b^2 + y_b^2 x_b 1 | * -1/d | x_c^2 + y_c^2 x_c 1 |

where (x_a, y_a) , (x_b, y_b) , (x_c, y_c) are the coordinates of the triangle's vertices, and the denominator d is defined as

  | x_a y_a 1 | d = | x_b y_b 1 | * 2 | x_c y_c 1 |

And then there is Wikipedia with a richer set of formulas. For example, here .