How is the Pythagorean Theorem related to the Equation of a CircleMy teacher wants me...
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
Draw a circle with radius r and center at the origin. In polar coordinates, . is thus true.
The equation for a circle is
You can use the following diagram:
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.