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My teacher wants me to figure out how the Pythagorean Theorem and the Equation of a Circle are related. I can't figure this out because I view them as being two completely different things. I understand what the equation for a circle is, but how does that relate to the Pythagorean Theorem?

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  • $\begingroup$ Draw a circle with radius $r$ and center at the origin. In polar coordinates, $x=r\sin \theta,y=r\cos\theta$. $x^2+y^2=1$ is thus true. $\endgroup$
    – user122283
    May 25, 2014 at 2:56

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Draw a circle with radius $r$ and center at the origin. In polar coordinates, $x=r\sin \theta,y=r\cos\theta$. $x^2+y^2=1$ is thus true.

The equation for a circle is $(x-a)^2 + (y-b)^2 = r^2$. You can use the following diagram:

(From https://www.mathsisfun.com/algebra/circle-equations.html.)

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$$(x−a)^2+(y−b)^2=r^2$$

Look at the equation of a circle with center $(a,b)$ and radius $r$.

Consider the right triangle with sides $A = x-a, B = y-b$ and $C = r$. You see that the equation of the circle is just the Pythagorean theorem.

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