21. Consider the Pythagorean Theorem, the distance formula, and the equation of a circle with centre at the origin and radius \( r \).
Pythagorean Theorem: \( a^{2}+b^{2}=c^{2} \)
Distance formula: \( D=\sqrt{\left(x_{2}-x_{1}\right)^{2}+\left(y_{2}-y_{1}\right)^{2}} \)
Equation of a circle: \( x^{2}+y^{2}=r^{2} \)
Explain using words and graphs how each of these formulas is related to one another. To help you, think about a triangle with vertices \( A(3,4), B(3,0) \), and \( C(0,0) \). Think about the hypotenuse, the distance from the origin to point \( A \), and the radius of the circle.
Use as much detail as possible in your response.
