Coordinate Geometry: JEE Main 2023 Mathematics question

If the point $\left(\alpha, \frac{7 \sqrt{3}}{3}\right)$ lies on the curve traced by the mid-points of the line segments of the lines $x \cos \theta+y \sin \theta=7, \theta \in\left(0, \frac{\pi}{2}\right)$ between the co-ordinates axes, then $\alpha$ is equal to :