"The Distance Formula is actually the Pythagorean Theorem unsquared. Instead of d^2 (c^2) it's just d and (x1-x2)^2 and (y1-y2)^2 are a^2 and b^2. The equation of a circle is the Pythagorean Theorem. (x - h)^2 is a^2 and (y - k)^2 is b^2, while the radius squared is c^2."
"They are all in some way forms of the Pythagorean Theorem, and they can all be used to find the distance between two points on a graph."
"They all tell the distance of something. The Distance formula tells the distance of point A to point B. The Pythagorean theorem tells the length or distance of side C. And the equation of a circle calculates the distance of points from the center of the circle."
Good one for the the Pythagorean Theorem - Distance formula link:
"The distance formula is related to the Pythagorean Theorem because they both find distance. The distance formula uses coordinates and the Pythagorean Theorem uses already known lengths, which can all be found by using coordinates."
Good one for the Distance Formula - Circle Equation link:
The equation of a circle is the distance formula, just after squaring both sides to make it d^2 = (x1-x2)^2 + (y1-y2)^2. This is because when you are graphing a circle, the point it is centered around, or (h, k), is the same as (x2, y2). Also, the radius (r^2) is just the distance from the center of the circle to any point on the circle.
And best of all...
"The distance formula is like the pythagorean theorem because finding the distance between two points is the same as finding the hypotenuse of a triangle if the two points were the legs of the triangle. It is related to the equation of a circle because in a circle you are finding points at a certain distance away from the middle."
Think about your answer. How does it compare for completeness and clarity?