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if the centre and radius of a circle is (3,4) and 7 units respectively, then what is the position of the point A(5,8) with respect to circle?

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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,


\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 = √(( x_2- x_1)^2 + ( y_2- y_1)^2) \\\\\\ d=√((5-3)^2+(8-4)^2)\implies d=√((-2)^2+4^2)\implies d=√(4+16) \\\\\\ d=√(20)\implies d\approx 4.472136

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.
User Fionnuala
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