A circle passes thru three pts A , B and C with line segment AC as diameter . A line passing thru A intersects the chord BC at a pt. D inside the circle. If angles DAB and CAB are α and β , respectively and the distance b/w pt. A and the mid pt. of line segment DC is d , prove that the area of the circle is ( π d2 cos2 α) / ( cos2 α + cos 2 β + 2 cos α cos β cos ( β - α ) ).
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