Question

How to find a point is inside a circle or not?

Answer 1

It's very simple to find whether a point is inside the circle or not , Just remember these simple steps -

1. Observe the location of point , If the point is inside the round boundary of circle it's clearly Inside it or in the interior of cirlce.

2. If the point lies anywhere outside the boundary of cirlce , Then that point will be outside or in the exterior of cirlce.

3. An interesting case , What can say if the point lies on Boundary of cirlce? It's still inside or in the interior of cirlce, The reason behind this is practical, Consider any house with a circular boundary, or any shape , because it applies to all , You keep something on the boundary of your house , Is it outside of your home?, absolutely not , It'll still be considered inside your home , In the same way any point lying on the boundary of a circle falls in interior of the Cirlce.
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Answer 2

let equation of circle ; x² + y² + 2gx + 2fy + c ,
   concept : if any point (α,β), put in equation of circle then we 
condition (1) :-  α² +β² +2gα +2fβ + c > 0 then, point must be lies in outside of circle.
condition(2) :-α² +β² +2gα +2fβ + c < 0 then, point must be lies in inside of circle .
condition(3) :-α² +β² +2gα +2fβ + c =0 then, point lies on circumference of circle.