Position of a Point With Respect to Circle - Practice Questions & MCQ

Position of a Point With Respect to Circle

Let S be a circle and P be any point in the plane.Then

To check if the point P (x₁, y₁) lies outside, on or inside the circle S 

• If CP² - r² > 0, then CP is greater than r, which means P lies outside the circle
• If CP² - r² < 0, then CP is lesser than r, which means P lies inside the circle
• If CP² - r² = 0, then CP is equal to r, which means P lies on the circle

Let us find the equation for CP² - r²

This expression can also be obtained by substituing the coordinates of point P in the equation of the circle, and we call this expression S₁

So, if

Greatest and Least Distance of a Point from a Circle

S₁ be a circle and P be any point in the plane.

(a) If P lies inside of the circle

The minimum distance of P from the circle = PA = AC - PC =  r - PC  

The maximum distance of P from the circle = PB = BC + PC = r + PC 

(b) If P lies outside of the circle

The minimum distance of P from the circle = PA = CP - AC = CP - r

The maximum distance of P from the circle = PB = BC + PC = r + PC