## Equation of a circle – Demonstration

**Let’s consider circle with as circle’s center and the circle’s radius.**

**The perimeter of circle is the geometric locus for the point , function of and . The circle’s equation is the expression that it is true for any .**

**Using Pythagoras theorem for the right triangle we have:**

**[1] where:**

**[2] **

**[3] **

**[4] **

**By replacing the values we have for the different segment lines ([2], [3], and [4]) into [1] we get ****the general form of circle’s equation:**

## [5]

**When the center of the circle is coincident with the Origin of the Cartesian Coordinate System (** O(0, 0)** ), and , [5] becomes:**

## [6]

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