Lines $L_1: y-x=0$ and $L_2: 2 x+y=0$ 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 I The ratio $P R: R Q$ equals $2 \sqrt{2}: \sqrt{5}$. Statement II In any triangle, bisector of an angle divides the triangle into two similar triangles.

• A

  Statement I is true, Statement II is true; Statement II is a correct explanation for Statement I
• Correct answer
  B

  Statement I is true, Statement II is true; Statement II is not a correct explanation for Statement I
• C

  Statement I is true, Statement II is false
• D

  Statement I is false, Statement II is true

Solution

In $\triangle O P Q$
Clearly, $$ \frac{P R}{R Q}=\frac{O P}{O Q}=\frac{2 \sqrt{2}}{\sqrt{5}} $$

Hence, the correct answer is option: 'B'.