question_answer

 The coordinates of the circumcentre of the triangle formed by the points \[O(0,0),\]\[A(a,0)\] and \[B(0,b)\] are:

A) \[(a,b)\]

B) \[\left( \frac{a}{2},\frac{b}{2} \right)\]

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

D) \[(b,a)\]

Correct Answer: B

Solution :

[b] Since \[\angle AOB=90{}^\circ \]and O is a point on the circle.So, AB is a diameter of the circle.

\[\therefore \] Circumcentre is the mid-point of diameter AB

\[=\left( \frac{a+0}{2},\frac{0+b}{2} \right)\] i.e., \[\left( \frac{a}{2},\frac{b}{2} \right)\]