How is the Pythagorean Theorem related to the Equation of a CircleMy teacher wants me...

Leonel Contreras

Leonel Contreras

Answered

2022-06-24

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

Answer & Explanation

Lilliana Burton

Lilliana Burton

Expert

2022-06-25Added 19 answers

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

Dale Tate

Expert

2022-06-26Added 5 answers

( 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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