Question

Lines $L_1:y-x=0$ and $L_2:2x+y=0$ intersect the line $L_3:y+2=0$ at $P$ and $Q$, respectively. The bisector of the acute angle between $L_1$ and $L_2$ intersects $L_3$ at R.

STATEMENT-1 : The ratio $PR:RQ$ equals $2\sqrt{2}:\sqrt{5}.$
because

STATEMENT-2: In any triangle, bisector of an angle divides the triangle into two similar triangles.

• A. Statement- 1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1
• B. Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1
• C. Statement-1 is True, Statement -2 is False
  
• D. Statement-1 is False, Statement-2 is True.
  

Answer 1

The correct option is C Statement-1 is True, Statement -2 is False


Point of intersection of $L_1\text{and}{L}_2$ is $A(0,0)$.
Also $P(-2,-2),Q(1,-2)$

$\because$ AR is the bisector of $\angle PAQ$ therefore $R$ divides $PQ$ in the same ratio as $AP:AQ$.
Thus $PR:RQ=AP:AQ=2\sqrt{2}:\sqrt{5}\therefore$ Statement - 1 is true.
Statement-2 is clearly false.