The circle c has the centre at (3,2) and passes through the point (2,1) determine whether the point with coordinates(4,7) lies on or in the circle ?

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Answer 1 · 2017-10-15T10:26:07

the point $(4;7)$ is external to the circle

Let's find the radius by calculating the distance between the center and the given point belonging to the circle:

$r=sqrt((x_P-x_C)^2+(y_P-y_C)^2)$

Let $P=(2;1)$ and $C=(3;2)$

Then $r=sqrt((2-3)^2+(1-2)^2)=sqrt2$

The distance between the center C and the point $(4;7)$ is

$d=sqrt((4-3)^2+(7-2)^2)=sqrt26$
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Since $d>r$ we conclude that the point $(4;7)$ is external to the circle