1.

Lines L_(1) : y-c=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 I The ratio PR : RQ equals 2sqrt(2) : sqrt(5). Because Statement II In any triangle, bisector of an angle divides the triangle into two similar triangles.

Answer»

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

Solution :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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