The points (2,3) and (3,2) lie on a circle whose center is on the x-axis. What is the radius of the circle?
+2668 Because of the shape of a circle, both the points have to be the same distance from the center.
Using the Pythagorean theorem, we can write this as an equation: \(\sqrt{(2-x)^2 + (3-y)^2} = \sqrt{(3-x)^2+(2-y)^2}\)
Substituting 0 for y, we get: \((2-x)^2 +9 = (3-x)^2+4\)
Solving, we find \(x = 0\), meaning the coordinates of the center are: \((0, 0)\)
Using the Pythagorean Theorem, we find that the radius of the circle is \(\color{brown}\boxed{\sqrt{13}}\)
+2668 Because of the shape of a circle, both the points have to be the same distance from the center.
Using the Pythagorean theorem, we can write this as an equation: \(\sqrt{(2-x)^2 + (3-y)^2} = \sqrt{(3-x)^2+(2-y)^2}\)
Substituting 0 for y, we get: \((2-x)^2 +9 = (3-x)^2+4\)
Solving, we find \(x = 0\), meaning the coordinates of the center are: \((0, 0)\)
Using the Pythagorean Theorem, we find that the radius of the circle is \(\color{brown}\boxed{\sqrt{13}}\)
