The incentre of a triangle with vertices (7,1),(-1,5) and (3+2 √3, 3+4 √3) is

Question

The incentre of a triangle with vertices (7,1),(-1,5) and (3+2 √3, 3+4 √3) is (A) (3+(2/√3), 3+(4/√3)) (B) (1+(2/3 √3), 1+(4/3 √3)) (C) (7,1) (D) None of these

Tardigrade Admin · Accepted Answer

<img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/mathematics/c82de5a82c9470acb11e4b93671ea39f-.png" /> ∵ AB = BC = CA = 4√5, i.e., given triangle is equilateral. (Incentre of a triangle are same as the centroid when triangle is equilateral) Hence, incentre =((7-1+3+2 √3/3), (1+5+3+4 √3/3)) =(3+(2/√3), 3+(4/√3))

Q. The incentre of a triangle with vertices $(7, 1), (- 1, 5)$ and $(3 + 23, 3 + 43)$ is

$(3 + \frac{2}{3}, 3 + \frac{4}{3})$

$(1 + \frac{2}{3 3}, 1 + \frac{4}{3 3})$

$(7, 1)$

None of these

$∵ A B = BC = C A = 45$ ,
i.e., given triangle is equilateral. (Incentre of a triangle are same as the centroid when triangle is equilateral)
Hence, incentre $= (\frac{7 - 1 + 3 + 2 3}{3}, \frac{1 + 5 + 3 + 4 3}{3})$
$= (3 + \frac{2}{3}, 3 + \frac{4}{3})$

Q. The incentre of a triangle with vertices (7,1),(−1,5) and (3+23​,3+43​) is

(3+3​2​,3+3​4​)

(1+33​2​,1+33​4​)

(7,1)