AIEEE 2011 Solved Paper

L1:y−x=0
L2:2x+y=0
L3:y+2=0
On solving the equation of line L1 and L2 we get their point of
intersection (0,0) i.e., origin O.
On solving the equation of line L1 and L3,
we get P=(−2,−2).
Similarly, we get Q=(−1,−2)
We know that bisector of an angle of a triangle, divide the opposite side the triangle in the ratio of the sides including the angle [ Angle Bisector Theorem of a Triangle ]
‌∴‌

PR

RQ

=‌

OP

OQ

=‌

√(−2)2+(−2)2

√(−1)2+(−2)2

‌=‌

2√2

√5