Minimum distance for ant avoiding repellents

To avoid going within 1 metre of B and C, the ant must travel along circular arcs of radius 1 m centered at B and C. From A, the ant follows a quarter arc of radius 1 centered at B to point P (angle $90^\circ$): arc length $= \frac{90^\circ}{360^\circ} \times 2\pi(1) = \frac{\pi}{2}$. From P to Q, it moves along a straight tangent segment of length $1$ m. From Q to D, it follows another quarter arc centered at C: arc length $= \frac{\pi}{2}$. Total minimum distance $= \frac{\pi}{2} + 1 + \frac{\pi}{2} = 1 + \pi$.