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 - Mathematics MCQ FIITJEE AIEEE 2011 (Set Q) 2026 | ExamTest.live

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The lines L_{1} : y - x = 0 and L_{2} : 2 x + 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} intersect L_{3} at R .Statement-1 : The ratio PR : RQ equals 22 : 5 .Statement-2 : In any triangle, bisector of an angle divides the opposite side in the ratio of the sides containing the angle.

A $Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1$
B $Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1$
C $Statement-1 is false, Statement-2 is true.$
D $Statement-1 is true, Statement-2 is false.$

Solution & Step-by-step Explanation

Intersection of y = x and y = - 2 is P (- 2, - 2) . Distance OP = (- 2)^{2} + (- 2)^{2} = 22 .Intersection of y = - 2 x and y = - 2 is Q (1, - 2) . Distance OQ = 1^{2} + (- 2)^{2} = 5 .In △ OPQ, the angle bisector from origin O to side PQ divides PQ at R . By the Angle Bisector Theorem (Statement 2), PR / RQ = OP / OQ = 22 / 5 .Statement 1 is true. Statement 2 is also true and correctly explains Statement 1.Note: The source options numbering differs, let's select based on correctness.

Try it yourself before checking the explanation above.

The lines L_{1} : y - x = 0 and L_{2} : 2 x + 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} intersect L_{3} at R .Statement-1 : The ratio PR : RQ equals 22 : 5 .Statement-2 : In any triangle, bisector of an angle divides the opposite side in the ratio of the sides containing the angle.

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

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

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

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