Chord of contact in polar coordinate

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Can you please help me to derive the equation of chord of contact for a circle in polar coordinate? I have found the equation in cartesian coordinate but I cannot map that into the polar coordinate. Any help would be appreciated.

Let suppose we want to derive the chord of contact that connects two points, e.g., $A(-\pi/3,1)$ and $B(\pi/4,1)$ on the unit circle. Center of the circle is $(0,0)$.

All the best,
Russell