JEE Main 2026 · 4 Apr · Shift 1 · Mathematics Q11

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MathematicsSingle correct+4 / -1Question 11 of 75

Let the line $L_1:x+3=0$ intersect the lines $L_2:x-y=0$ and $L_3:3x+y=0$ at the points A and B, respectively. Let the bisector of the obtuse angle between the lines $L_2$ and $L_3$ intersect the line $L_1$ at the point C. Then $BC^2:AC^2$ is equal to:

5:1

1:5

2:3

3:2

Answer and worked solution

Official answer: A

Points. $A=(-3,-3)$ on $L_2$ and $B=(-3,9)$ on $L_3$ .

Angle AOB is obtuse: $\vec{OA}\cdot\vec{OB}=9-27<0$ . So its internal bisector is the obtuse-angle bisector, and it meets AB at C.

Angle bisector theorem. $\dfrac{BC}{AC}=\dfrac{OB}{OA}=\dfrac{\sqrt{90}}{\sqrt{18}}=\sqrt5$ , so $BC^2:AC^2=5:1$ .

(A)

Topics:Angle between lines

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JEE Main 2026 · 4 Apr · Shift 1, Mathematics question 11