question_answer

The vertices of a triangle are (3, 0), (3, 3) and (0, 3). Then, the coordinates of the circumcentre are

A)  (0, 0)                    

B)         (1, 1)

C)  \[\left( \frac{5}{2},\frac{5}{2} \right)\]           

D)         (2, 2)

E)  \[\left( \frac{3}{2},\frac{3}{2} \right)\]

Correct Answer: E

Solution :

Given vertices are the vertices of right angled triangle with\[\angle C=\frac{\pi }{2}\]. \[\therefore \]Coordinates of the circumcentre is the midpoint of AB ie, \[\left( \frac{3}{2},\frac{3}{2} \right)\].