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 :
If the triangle is equilateral, then incentre is coincide with centroid of the triangle. Let A \[(1,\sqrt{3})\], B(0, 0) and C(2, 0) be the vertices of a \[\Delta ABC\]. \[\therefore \] \[a=BC=\sqrt{{{(2-0)}^{2}}+{{(0-0)}^{2}}}=2\] \[b=AC=\sqrt{{{(2-1)}^{2}}+{{(0-\sqrt{3})}^{2}}}=2\] and \[c=AB=\sqrt{{{(0-1)}^{2}}+{{(0-\sqrt{3})}^{2}}}=2\] \[\therefore \] The triangle is an equilateral triangle. \[\therefore \] Incentre is same as centroid of the triangle. \[\Rightarrow \] Coordinates of incentre are \[\left( \frac{1+0+2}{3},\frac{\sqrt{3}+0+0}{3} \right)\] i.e., \[\left( 1,\frac{1}{\sqrt{3}} \right)\].
You need to login to perform this action.
You will be redirected in
3 sec
