How is the Pythagorean Theorem related to the Equation of a CircleMy 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?

Question

How is the Pythagorean Theorem related to the Equation of a CircleMy teacher wants me to figure out how the Pythagorean Theorem and the Equation of a Circle are related. I can&#039;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?

Lilliana Burton · Accepted Answer

Draw a circle with radius r and center at the origin. In polar coordinates,   x  =  r  sin  ⁡  θ  ,  y  =  r  cos  ⁡  θ.       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:

Dale Tate · Accepted Answer

(  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.