JEE Main 2026 · 4 Apr · Shift 2 · Mathematics Q23

← JEE Main 2026 · 4 Apr · Shift 2

MathematicsInteger+4 / -1Question 23 of 75

Let A, B be points on the two half-lines $x-\sqrt3|y|=\alpha$ , $\alpha>0$ at a distance of $\alpha$ from their point of intersection P. The line segment AB meets the angle bisector of the given half-lines at the point Q. If $PQ=\dfrac92$ and R is the radius of the circumcircle of $\Delta PAB$ , then $\dfrac{\alpha^2}R$ is equal to ________.

Your answer

Answer and worked solution

Official answer: 9

Geometry. The half-lines meet at $P(\alpha,0)$ at angles of $\pm30^\circ$ to the x-axis, so $\angle APB=60^\circ$ . With $PA=PB=\alpha$ , triangle PAB is equilateral.

Q is the midpoint of AB, so $PQ=\frac{\sqrt3}2\alpha=\frac92$ and $\alpha=3\sqrt3$ .

Circumradius. $R=\frac\alpha{\sqrt3}=3$ , so $\frac{\alpha^2}R=\frac{27}3=9$ .

Answer: 9

Topics:Angle between lines

← Previous question Next question →

JEE Main 2026 · 4 Apr · Shift 2, Mathematics question 23