we know the circle's center is at (3,4), and we know point A is at (5,8), let's get how far is A is from the center,
[tex]\bf ~~~~~~~~~~~~\textit{distance between 2 points}\\\\
\begin{array}{ccccccccc}
&&x_1&&y_1&&x_2&&y_2\\
% (a,b)
&\bigodot&(~ 3 &,& 4~)
% (c,d)
&A&(~ 5 &,& 8~)
\end{array}~~~
% distance value
d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2}
\\\\\\
d=\sqrt{(5-3)^2+(8-4)^2}\implies d=\sqrt{(-2)^2+4^2}\implies d=\sqrt{4+16}
\\\\\\
d=\sqrt{20}\implies d\approx 4.472136[/tex]
now, notice the distance "d", is really less than the radius, 7, therefore, point A is not 7 units away from the center, and is not "ON" the circle itself, and is not outside the circle either, is really inside it, just a few hops away from its center.
