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# Circumcenter Calculator

The circumcenter is the center point of the circumcircle drawn around a polygon. The circumcircle of a polygon is the circle that passes through all of its vertices and the center of that circle is called the circumcenter. All polygons that have circumcircle are known as cyclic polygons.

## What is a Circumcenter Calculator?

A 'Circumcenter Calculator' is a free online tool that calculates the coordinates for the circumcenter of a triangle. In this calculator, you can enter the coordinates of the triangle and the coordinate of circumcenter will be calculated within a few seconds.

## How to Use Circumcenter Calculator?

Follow the steps given below to use the calculator:

**Step 1:**Enter the coordinates of the triangle in the space provided.**Step 2:**Click on**"Calculate"**.**Step 3:**Click on**"Reset"**to clear the field and enter new values.

## How to Find a Circumcenter?

We calculate the circumcenter of the triangle using trigonometry.

If ABC is a triangle with coordinates (x_{1}, y_{1}), (x_{2}, y_{2}), and (x_{3}, y_{3}) then the coordinates of the circumcenter of the triangle will be:

**Circumcenter O(x, y) = [ {(x _{1}Sin2A + x_{2}Sin2B + x_{3}Sin2C) / (Sin2A + Sin2B + Sin2C)}, {(y_{1}Sin2A + y_{2}Sin2B + y_{3}Sin2C) / (Sin2A + Sin2B + Sin2C)} ] **

Here O is the circumcenter

And, Sin 2A, Sin2B, and Sin2C are Sin of double angles of Angle A, B, and C.

**Solved Example:**

What is the circumcentre of a triangle with coordinates (0.0), (0.4), and (4,0)?

**Solution:**

Here angle A is 90º and angle B and C are 45º

So, Sin2A = 0

Sin2B = Sin2C = 1

Now, circumcenter O(x, y) = [ {(x_{1}Sin2A + x_{2}Sin2B + x_{3}Sin2C) / (Sin2A + Sin2B + Sin2C)}, {(y_{1}Sin2A + y_{2}Sin2B + y_{3}Sin2C) / (Sin2A + Sin2B + Sin2C)} ]

= [2, 2]

Therefore, the circumcenter of the triangle with coordinates (0.0), (0.4), and (4,0) is [2, 2]

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