The line `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 `P R"":""R Q` equals `2sqrt(2):""sqrt(5)` Statement-2 : In any triangle, bisector of an angle divides the triangle into two similar triangles. Statement-1 is true, Statement-2 is true ; Statement-2 is correct explanation for Statement-1 Statement-1 is true, Statement-2 is true ; Statement-2 is not a correct explanation for Statement-1 Statement-1 is true, Statement-2 is false Statement-1 is false, Statement-2 is true

Options

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 statement1.
C. Statement 1 is true, statement 2 is true, statement 2 is not the correct explanation of statement 1.
D. Statement 1 is false, statement 2 is true.

Answer

A

Explanation

Draw lines on coordinate axes as shown here.

From the geometry of angle bisector,
`(PR)/(RQ) = (OP)/(OQ) = (2sqrt(2))/(sqrt(5))`