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The Circle [Solved!]

My question

Check out the url below. Under Plane Analytical Geometry - The Circle.

The final line in Example 4 solution box, you note that the circle passes through the origin and it is logical because the coordinates fit perfectly, i.e. the sum of the square of each coordinate will be equal to the radius squared.

For clarification, what is the logic behind it?

Relevant page

3. The Circle

What I've done so far

We know that if the center of the circle is the origin then the coordinates will fit perfectly.

Are you saying that if the origin falls anywhere on the circle, then that logic also applies?

X

Check out the url below.  Under Plane Analytical Geometry - The Circle.

The final line in Example 4 solution box, you note that the circle passes through the origin and it is logical because the coordinates fit perfectly, i.e. the sum of the square of each coordinate will be equal to the radius squared. 

For clarification, what is the logic behind it?
Relevant page

<a href="https://www.intmath.com/plane-analytic-geometry/3-circle.php">3. The Circle</a>

What I've done so far

We know that if the center of the circle is the origin then the coordinates will fit perfectly.

Are you saying that if the origin falls anywhere on the circle, then that logic also applies?

Re: The Circle

@Phinah: I have added some further explanation to my statement at the end of Example 4.

You may need to refresh the page to see the changes.

I hope it addresses your final question, "Are you saying that if the origin falls anywhere on the circle, then that logic also applies?"

X

@Phinah: I have added some further explanation to my statement at the end of Example 4. 

You may need to refresh the page to see the changes.

I hope it addresses your final question, "Are you saying that if the origin falls anywhere on the circle, then that logic also applies?"

Re: The Circle

Just reviewed it. Thanks. Very good addition to explain it.

X

Just reviewed it.  Thanks.  Very good addition to explain it.

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