The incentre of the triangle with vertices (1,√( 3) ), (0, 0) and (2, 0) is:

Q86 / 160 · TS EAMCET 2021 (04 Aug Shift 1) · Mathematics

The incentre of the triangle with vertices $(1, \sqrt{3}), (0, 0)$ and $(2, 0)$ is:

A
$(1, \frac{\sqrt{3}}{2})$
B
$(\frac{2}{3}, \frac{1}{\sqrt{3}})$
C
$(\frac{2}{3}, \frac{\sqrt{3}}{2})$
Correct answer
D
$(1, \frac{1}{\sqrt{3}})$

Solution

$A B = \sqrt{{(\sqrt{3} - 0)}^{2} + {(1 - 0)}^{2}} = 2$
$B C = \sqrt{{(0 - 0)}^{2} + {(2 - 0)}^{2}} = 2$
$A C = \sqrt{{(0 - \sqrt{3})}^{2} + {(2 - 1)}^{2}} = 2$
So, triangle is equilateral triangle.
So, the incentre is the same as the centroid.
Incentre
$= (\frac{1 + 0 + 2}{3}, \frac{\sqrt{3} + 0 + 0}{3}) = (1, \frac{1}{\sqrt{3}})$

Hence, the correct answer is option: 'D'.

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The incentre of the triangle with vertices (1, 3 ), (0, 0) and (2, 0) is:

Solution

Relevant Questions

The incentre of the triangle with vertices $(1, \sqrt{3}), (0, 0)$ and $(2, 0)$ is: