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.
STATEMENT-1:Then the ratio PR:RQ equals $2 \sqrt{2} : \sqrt{5}$ .
STATEMENTS-2 In any triangle, bisector of an angle divides the triangle into two similar triangles.

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Statement-1 is True Statement -2 is True; Statement-2 is a 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.

answer is C.

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Detailed Solution

Point of intersection of $L_{1}$ and is A (0,0)
Also P(-2,-2),Q(1,-2)
Question Image
$∵$ AR is the bisector of $< P A Q$ , therefore R divides
PQ in the ratio of AP:AQ.
i.e., PR:RQ=AP;AQ= $2 \sqrt{2} : \sqrt{5}$
$∴$ Statement-1 is true.
Statement-2 is clearly false.