Question 18Triangle $ABC$ has $AB = 27,$ $AC = 26,$ and $BC = 25.$ Let $I$ denote the intersection of the internal angle bisectors of $\triangle ABC.$ What is $BI?$$15$$5 + \sqrt{26} + 3\sqrt{3}$$3\sqrt{26}$$\dfrac{2}{3}\sqrt{546}$$9\sqrt{3}$