Let three lines L1,L2 and L3 belonging to the family x−2y+6+λ(x−y+2)=0 where λ is a parameter, be interior angle bisectors of △ABC. If the equation x+3y−4=0 represents side AB of the triangle, then the value of ⎡⎣△rcotA2+a+rcotB2+b+rcotC2+c⎤⎦ is (Note: Symbols used have usual meanings in △ABC and [.] denotes the greatest integer function.)

Let three lines L1,L2 and L3 belonging to the family x−2y+6+λ(x−y

1.	Let three lines L1,L2 and L3 belonging to the family x−2y+6+λ(x−y+2)=0 where λ is a parameter, be interior angle bisectors of △ABC. If the equation x+3y−4=0 represents side AB of the triangle, then the value of ⎡⎣△rcotA2+a+rcotB2+b+rcotC2+c⎤⎦ is (Note: Symbols used have usual meanings in △ABC and [.] denotes the greatest integer function.)
Answer» Let three lines $L_{1}, L_{2}$ and $L_{3}$ belonging to the family $x - 2 y + 6 + λ (x - y + 2) = 0$ where $λ$ is a parameter, be interior angle bisectors of $△ A B C .$ If the equation $x + 3 y - 4 = 0$ represents side $A B$ of the triangle, then the value of $⎡ ⎣ \frac{△}{r cot \frac{A}{2} + a + r cot \frac{B}{2} + b + r cot \frac{C}{2} + c} ⎤ ⎦$ is (Note: Symbols used have usual meanings in $△ A B C$ and $[.]$ denotes the greatest integer function.)