In a circle with centre O, suppose A, P,...

In a circle with centre O, suppose A, P, B are three points on its circumference such that P is the mid-point of minor arc AB. Suppose `angle AOB=theta` `(Area(triangle AOB))/(Area(triangle APB))=sqrt (5)+2` If `angle AOB` is doubled to `2theta`, then the ratio `(area ( triangle AOB)) /(area(triangle APB))` is

A

`1/sqrt5`

B

`sqrt 5 -2`

C

`2sqrt3 + 3`

D

`(sqrt5 - 1)/2`

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The correct Answer is:

A

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