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The line L1:""y""-""x""=""0 and L2:""2x"...

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

A

Statement I is true, Statement II is also true, Statement II is correct explanation of Statement I

B

Statement I is true, Statement II is also true, Statement II is not the correct explanation of Statement I

C

Statement I is true , Statement II is false

D

Statement I is false , Statement II is true

Text Solution

Verified by Experts

It is not necessary that the bisector of an angle will divide the triangle into two similar triangles, therefore, statements II is false.
Now, we verify Statement I.
`DeltaOPQ`, `OR` is the internal bisector of `/_POQ`.
`:. (PR)/(RQ)=(OP)/(OQ)`
`implies(PR)/(RQ)=(sqrt(2^(2)+2^(2)))/(sqrt(1^(2)+2^(2)))=(2sqrt(2))/(sqrt(5))`
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