HOW TO FIND RADIUS OF CIRCLE WITH 2 END POINTS

Problem 1 :

The endpoints of diameter of circle are (2, 4) and (-3, -1). Find the radius of the circle ?

Solution :

Let the given points be A(2, 4) and B(-3, -1).

Distance between two end points of the diameter = diameter of the circle

Length of AB / 2 ==> Radius of the circle

Problem 2 :

Find the coordinate of center of the circle passing through the points A(1, 2), B(3, -4) and C(5, -6). Also find the radius of the circle ?

Solution :

Let the center point be O(a, b)

Distance between 

OA = OB = OC  (radii of circle)

(1) - (2)

(a - 3b) - (a - 2b) = 4 - 7

-3b + 2b = -3

b = 3

Applying the value of b in (1), we get

a - 3(3) = 4

a = 4 + 9

a = 13

So, the center is O(13, 3).

Problem 3 :

If the diameter of the circle of length 10 units which is having endpoints 

A(0, −3) and B(8, p)

find the possible values of p.

Solution :

Problem 4 :

If the points A(4, 3) and B(x, 5) are on the circle with center O(2, 3). Find the value of x.

Solution :

Distance between center and point of the boundary will be the measure of radius.

x² - 4x + 8 - 4 = 0

x² - 4x + 4 = 0

(x - 2)(x - 2) = 0

x = 2 and x = 2

Problem 5 :

The center of the circle is (2a - 1, 3a + 1) and it passes through the point (-3, -1). If the diameter of the circle is of length 20 units, find the value of a.

Solution :

Distance between center and the point (-3, -1) = radius of the circle 

radius = 20/2 ==>  10

So, the value of a is 2.