Centre of Circle Calculator

Centre = Intersection of Perpendicular Bisectors

\[ \text{Centre} = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right) \text{ for perpendicular bisector of chord} \]

Point 1 X-coordinate:

Point 1 Y-coordinate:

Point 2 X-coordinate:

Point 2 Y-coordinate:

Point 3 X-coordinate:

Point 3 Y-coordinate:

Centre of Circle:

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1. What is the Centre of a Circle?

The centre of a circle is the point equidistant from all points on the circumference. It can be found as the intersection point of perpendicular bisectors of any two chords of the circle.

2. How Does the Calculator Work?

The calculator uses the perpendicular bisector method:

\[ \text{Centre} = \text{Intersection of perpendicular bisectors of two chords} \]

Where:

Perpendicular bisector of a chord passes through the circle's centre
The intersection of two such bisectors gives the exact centre
Coordinates of three points on the circle are required

Explanation: For any chord of a circle, the perpendicular bisector will always pass through the centre of the circle. By finding two such bisectors, their intersection point gives us the centre.

3. Importance of Finding the Centre

Details: Determining the centre of a circle is fundamental in geometry, engineering, and design applications. It helps in calculating radius, diameter, and other circle properties, and is essential in construction and manufacturing processes.

4. Using the Calculator

Tips: Enter the coordinates of three distinct points on the circle. The points should not be collinear (on a straight line) for accurate results.

5. Frequently Asked Questions (FAQ)

Q1: Why do I need three points to find the centre?
A: Two chords are needed to find two perpendicular bisectors, and three points are required to define these two chords.

Q2: What if the points are collinear?
A: If the three points lie on a straight line, they don't define a circle, and the calculator won't provide a valid result.

Q3: Can I use this method for any circle?
A: Yes, this method works for any circle as long as the three points are distinct and not collinear.

Q4: How accurate is this calculation?
A: The calculation is mathematically precise, though rounding may occur in the displayed result.

Q5: Are there other methods to find the centre?
A: Yes, other methods include using the intersection of diameters or using the circle's equation, but the perpendicular bisector method is one of the most straightforward geometric approaches.