The lines L1 : y – x = 0 and L2 : 2x + y = 0 intersect the line L3 : y + 2 = 0 at P and Q respectively. The bisector of the acute between L1 and L2 intersects L3 at R. Statement-1 : The ratio PR : RQ equals 2 \sqrt{2} \textrm{ }\textrm{ } : \textrm{ }\textrm{ } \sqrt{5} Statement -2 : In any triangle, bisector of an angle divides the triangle into two similar triangle.

Engineering

Mathematics

angle bisector between two lines

Question

The lines L₁ : y – x = 0 and L₂ : 2x + y = 0 intersect the line L₃ : y + 2 = 0 at P and Q respectively. The bisector of the acute between L₁ and L₂ intersects L₃ 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 triangle.

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

Statement-1 is true, Statement-2 is true and Statement-2 is the correct explanation of Statement-1.

Statement-1 is true, Statement-2 is false and Statement-2 is not the correct explanation of Statement-1

Statement-1 is true, Statement-2 is false

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\ $AD:DB = 2\sqrt 2 :\sqrt 5 $

Q OD is angle bisector of angle AOB

\ St : 1 true

St : 2 false (obvious)

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