question_answer

The 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. Statements 1 : The ratio PR : RQ equals \[2\sqrt{2}:\sqrt{5}\]. Statement 2 : In any traingle, bisector of an angle divides the triangle into two similar triangles.   AIEEE  Solved  Paper-2011

A) Statement-1 is true, Statement-2 is false

B) Statement-1 is true, Statement-2 is true; Statement-2 is the correct explanation of Statement-1

C) Statement-1 is true, Statement-2 is true; Statement-2 is the not the correct explanation of Statement-1

D) Statement-1 is false, Statement-2 is true

Correct Answer: D

Solution :

             The figure is self explanatory               \[\frac{PR}{RQ}=\frac{OP}{OQ}=\frac{2\sqrt{2}}{\sqrt{5}}\] Statement-2 is false