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 and L_2 intersects L_3 at R. STATEMENT-1 : The ratio PR : RQ equals 2 2 : 5 . because STATEMENT-2 : In any triangle, bisector of an angle divides the triangle into two similar triangles.

JEE Advanced 2007 Mathematics question

Lines : y − x = 0 and : 2x + y = 0 intersect the line : y + 2 = 0 at P and Q, respectively. The bisector of the acute angle between and intersects at R. STATEMENT-1 : The ratio PR : RQ equals . because STATEMENT-2 : In any triangle, bisector of an angle divides the triangle into two similar triangles.

(A)Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1
(B)Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1
(C)Statement-1 is True, Statement-2 is FalseCorrect
(D)Statement-1 is False, Statement-2 is True

Answer: (C)

Solution

P = (−2, −2) on and Q = (1, −2) on ; both lines pass through O(0, 0). In triangle OPQ the angle at O is acute (the lines make 45° and about 116.6° with the x-axis, a difference of about 71.6°), so the bisector of the acute angle is the internal bisector at O, meeting

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Question ID VK-037526