Eduprobe
Question:
The line 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 angle between L1 and L2 intersects L3 at R. Statement-1: The ratio PR:RQ equals 2√2:√5. Statement-2: In any triangle, the bisector of an angle divides the triangle into two similar triangles. A. Statement-1 is true, Statement-2 is true, Statement-2 is not a correct explanation for Statement-1. B. Statement-1 is true, Statement-2 is false. C. Statement-1 is true, Statement-2 is true, Statement-2 is a correct explanation for Statement-1. D. Statement-1 is false, Statement-2 is true.
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 true, Statement-2 is true, Statement-2 is a correct explanation for Statement-1.
Statement-1 is false, Statement-2 is true.
Solution:
Intersection of L1 and L3 is P = (-2, -2)
Intersection of L2 and L3 is Q = (1, -2)
Now, Intersection of L1 and L2 is O = (0, 0)
Equation of angular bisector of ΔOPQ will be (√5 + 2√2)x = (√5 - √2)y
In ΔOPQ, the angle bisector of O divides PQ in the ratio of OP:OQ which is 2√2:√5 but it does not divide the triangle into two similar triangles.
Hence, option 'A' is correct.