CAT 2017 Quantitative Ability

Centroid, incenter, circumcenter and orthocenter are collinear ⇒ Triangle is isosceles ⇒ two sides must be equal. AB is the longest side⇒ the other two sides must be equal Sides should be 8, y and y.
Perimeter = 8 + 2y, s = 4 + y

$24=\sqrt{4^2\left({\mathit{y}}^2-16\right)}$
$24=4\sqrt{{\mathit{y}}^2-16}$
$6=\sqrt{{\mathit{y}}^2-16}$
${\mathit{y}}^2=52$
$\Rightarrow \mathit{y}=\sqrt{52}$
$\mathit{y}=2\sqrt{13}$