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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 -1 is True , Statement - 2 is true , Statement- 2 is a correct explanation for statement - 13

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 .

Text Solution

Verified by Experts

The correct Answer is:
C
Statement-2 is not true
In `DeltaOPQ` , OR is the bisector of `anglePOQ` .
`therefore (OP)/(OQ) = (PR)/(RQ) `
`[{:( because "Bisector of an angle divides") , ("opposite side in the ratio of ") , ("the sides containing the angle "):}]`
`implies (PR)/(RQ) = (2sqrt2)/(5)`
So , statement - 1 is true .
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