Multiple choice

A verticle pole stands at a point $'A'$ on boundry of a circle park of radius $a$ and blinds an angle $\alpha$ at another point $B$ on the boundry. If the cord $AB$ subtend angle $\alpha $ at the centre of the park, the height of pole is:

  1. $2a\cos \dfrac {\alpha }{2}\cot \alpha$
  2. $2a\sin \dfrac {\alpha }{2}\tan \alpha$
  3. $2a\cos \dfrac {\alpha }{2}\tan \alpha$
  4. $2a\sin \dfrac {\alpha }{2}\cot \alpha$
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