Question

The point (8,-4) lies on a circle. What is the length of the radius of this circle if the center is located at (5,-7)

Answer 1

notice the picture, the radius is just the distance from the
center to a point on the circle, thus





`\bf \begin{array}{llll} d = &\sqrt{({{ 8}}-{{ 5}})^2 + ({{ -4}}-{{(-7)}})^2}\\ &\qquad \uparrow \\ &radius \end{array} \\\\\\ d=√((3)^2+(-4+7)^2)\implies d=√(3^2+3^2)\implies d=√(18) \\\\\\ d=√(9\cdot 2)\implies d=√(3^2\cdot 2)\implies d=3√(2)`