INSIDE OUTSIDE OR ON THE CIRCLE

About "Inside outside or on the circle"

Inside outside or on the circle :

Here we are going to see how to determine if a point is inside or outside a circle.

Length of the tangent = √ (x₁² + y₁² + 2gx₁ +2fy₁ + c)

To check if the given point lie on the circle, inside the circle or out side the circle, we use the formula for length of tangent.

Example 1 :

Determine whether the points (− 2, 1), (0, 0) and (4, − 3) lie outside, on or inside the circle x² + y² − 5x + 2y − 5 = 0

Solution :

(i)  First let us check where does the point (-2, 1) lie on the circle  x² + y² − 5x + 2y − 5 = 0

 PT  =  √(x₁² + y₁² + 2gx₁ +2fy₁ + c)

here x₁  =  -2 and y₁  =  1

PT  =  √((-2)² + 1² − 5(-2) + 2(1) − 5)

PT²  =  (4 + 1 + 10 + 2 − 5)

PT²  =  (17 − 5)

PT²  =  12 > 0

Hence the point (-2, 1) lies outside the circle.

(ii)  (0, 0)

here x₁  =  0 and y₁  =  0

PT  =  √((0)² + 0² − 5(0) + 2(0) − 5)

PT²  =  (0 + 0 − 0 + 2 − 5)

PT²  =  -3 < 0

Hence the point (0, 0) lies inside the circle.

(ii)  (4, -3)

here x₁  =  4 and y₁  =  -3

PT  =  √(4² + (-3)² − 5(4) + 2(-3) − 5)

PT²  =  (16 + 9 − 20 - 6 − 5)

PT²  =  25 - 20 - 6 - 5

=  20 - 31

=  -11 < 0

Hence the point (4, -3) lies inside the circle.

Related pages

• How to find the length of tangent
• How to determine if a point is inside or outside a circle
• Find the equation of the tangent to the circle at the point
• How to find the point of intersection of circle and line
• How to prove if a line is tangent to a circle

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