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A circle passes through three points A, ...

A circle passes through three points A, B and C with the line segment AC as its diameter. A line passing through A intersects the chord BC at a point D inside the circle.If angles DAB and CAB are `alpha` and `beta` respectively and the distance between the point A and the mid-point of the line segment DC is d, prove that the area of the circle is `(pid^2cos^2a)/(cos^2alpha+cos^2beta+2cosalphacosbetacos(beta-alpha)`

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