Question

Find the circumcentre of the triangle whose vertices are (–2, –3), (–1, 0) and (7, –6). Also find the radius of the circumcircle.

Solution

Correct option is

5 units

 

Let A ≡ (–2, –3), B ≡ (–1, 0) and C ≡ (7, –6). Let P ≡ (xy) be the circumcentre of ∆ABC.                    

Since P is the circumcentre

 

        

                                              

                                                         

Taking first two numbers, we get 

          

and taking 1st and last member then, we get 

        

Solving (i) and (ii), we get 

        

Hence circumcentre is (3, –3). 

Radius of the circumcircle                                               

                                             .

SIMILAR QUESTIONS

Q1

 

Find the cartesian co-ordinates of the points whose polar coordinates are

                                     

Q2

 

Find the cartesian co-ordinates of the points whose polar coordinates are

            

Q3

Find the polar coordinates of the points whose cartesian coordinates are (–2, 2)

Q4

Find the polar coordinates of the points whose cartesian coordinates are (–3, 4)

Q5

Transform the equation  into cartesian form.

Q6

Transform the equation  into polar form.

Q7

 

Find the distance between the points

            

where a > 0.

Q8

An equilateral triangle has one vertex at the point (0, 0) and another at . Find the coordinates of the third vertyex. 

Q9

Let the opposite angular points of a square be (3, 4) and (1, –1). Find the coordinates of the remaining angular points

Q10

Find the coordinates of the point which divides the line segment joining the points (5, –2) and (9, 6) in the ratio 3 : 1.