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.

Statement-1 : The ratio PR:RQ\; equals\; 2\sqrt{2}:\sqrt{5}.

Statement-2 : In any triangle, bisector of an angle divides the triangle into two similar triangles.

  • Option 1)

    Statement-1 is true, Statement-2 is false.

  • Option 2)

    Statement-1 is false, Statement-2 is true.

  • Option 3)

    Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.

  • Option 4)

    Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1.

 

Answers (1)

As we learnt in 

Angle Bisector -

A line segment that bisects an angle of a triangle.

- wherein

 

 For point P: y-x=0 and y+2=0

So P is (2,-2)

 For point Q: 2x+y=0 and y+2=0

So Q is (-1, -2)

OP=2\sqrt{2} \: \: \: and \: \: OQ=\sqrt{5}

So, \frac{OP}{OQ}=\frac{PR}{RQ}=\frac{2\sqrt{2}}{\sqrt{5}} \: \: (property \: of \: angle \: bisector)

But statement 2 is false


Option 1)

Statement-1 is true, Statement-2 is false.

This option is correct

Option 2)

Statement-1 is false, Statement-2 is true.

This option is incorrect

Option 3)

Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.

This option is incorrect

Option 4)

Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1.

This option is incorrect

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