Question

The center is (9, 10), and the point on the circle is (7,4). what is the radius

Answer 1

well, let's recall what a radius is, is simply the distance from the center of a circle to a point on that circle, so the distance between those two points is the radius

`~~~~~~~~~~~~\textit{distance between 2 points} \\\\ (\stackrel{x_1}{9}~,~\stackrel{y_1}{10})\qquad (\stackrel{x_2}{7}~,~\stackrel{y_2}{4})\qquad \qquad d = √(( x_2- x_1)^2 + ( y_2- y_1)^2) \\\\\\ \stackrel{ radius }{r}=√((~~7 - 9~~)^2 + (~~4 - 10~~)^2) \implies r=√(( -2 )^2 + ( -6 )^2) \\\\\\ r=√( 4 + 36 ) \implies r=√( 40 )\implies r\approx 6.32`