Let \( A \) and \( B \) be two points on the circle \( |z|=r \) represented by \( z_{1} \) and \...

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Let \( A \) and \( B \) be two points on the circle \( |z|=r \) represented by \( z_{1} \) and \( z_{2} \) respectively then find the complex number representing the point of intersection of the tangents at \( A \) and \( B \) ?
(a) \( \frac{2 z_{1} z_{2}}{z_{1}+z_{2}} \)
(b) \( \frac{2 z_{1}}{z_{1}+z_{2}} \)
(c) \( \frac{2 z_{2}}{z_{1}+z_{2}} \)
(d) \( \frac{2 z_{1}}{z_{2}} \)
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