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

Question

The incentre of the triangle having the vertices (1, √3),(0,0) and (2,0) is (A) (1, (√3/2)) (B) ((2/3), (1/√3)) (C) ((2/3), (√3/2)) (D) (1, (1/√3))

Tardigrade Admin · Accepted Answer

O A=2 O B=√1+3=2 A B=√1+3=2 <img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/mathematics/bd11d37a45757f01f268acba8539888b-.png" /> O A=O B=A B ∴ Triangle is equilateral. Incentre ((0+2+1/3), (0+0+√3/3))=(1, (1/√3))

Q. The incentre of the triangle having the vertices $(1, 3), (0, 0)$ and $(2, 0)$ is

$(1, \frac{3}{2})$

$(\frac{2}{3}, \frac{1}{3})$

$(\frac{2}{3}, \frac{3}{2})$

$(1, \frac{1}{3})$

$O A = 2$
$OB = 1 + 3 = 2$
$A B = 1 + 3 = 2$

$O A = OB = A B$
$∴$ Triangle is equilateral.
Incentre $(\frac{0 + 2 + 1}{3}, \frac{0 + 0 + 3}{3}) = (1, \frac{1}{3})$

Q. The incentre of the triangle having the vertices (1,3​),(0,0) and (2,0) is

(1,23​​)

(32​,3​1​)

(32​,23​​)

(1,3​1​)