Mathematics - Straight Lines Question with Solution | TestHub

Let three lines $I_1,I_2\&I_3$ belonging to the family $x-2y+6+\lambda (x-y+2)=0$, where $\lambda$ is a parameter, be interior angle bisectors of $△ABC$. If the equation $x+3y-4=0$ represents side AB of the triangle, then find the value of $\left[\frac{\Delta }{\sum \left(r\cot \frac{A}{2}+a\right)}\right]$ (where symbols used have usual meaning in $△ABC$ and $[$. denotes G.I.F.)