question_answer

The incentre of the triangle with vertices \[(1,\sqrt{3})\], (0, 0) and (2, 0) is    [IIT Screening 2000]

A) \[\left( 1,\frac{\sqrt{3}}{2} \right)\]

B) \[\left( \frac{2}{3},\frac{1}{\sqrt{3}} \right)\]

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

D) \[\left( 1,\frac{1}{\sqrt{3}} \right)\]

Correct Answer: D

Solution :

  Clearly, the triangle is equilateral. So, the incentre is the same as the centroid. \[\therefore \] Incentre \[=\,\left( \frac{1+0+2}{3},\,\,\frac{\sqrt{3}+0+0}{3} \right)=\left( 1,\,\frac{1}{\sqrt{3}} \right)\].