JEE Advance - Mathematics (1996 - No. 23)
A circle passes through three points A, B and C with the line segment AC as its diameter. A line passing through A 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 $$${{\pi \,{d^2}\,\,{{\cos }^2}\,\,\alpha } \over {{{\cos }^2}\,\alpha \, + \,{{\cos }^2}\,\beta \, + \,\,2\,\cos \,\,\alpha \,\,\cos \,\beta \,\cos \,\,(\beta - \alpha )\,}}$$$
$${{pi ,{d^2},,{{cos }^2},,alpha } over {{{cos }^2},alpha , + ,{{cos }^2},eta , + ,,2,cos ,,alpha ,,cos ,eta ,cos ,,(eta - alpha ),}}$$
$${{pi ,{d^2},,{{sin }^2},,alpha } over {{{cos }^2},alpha , + ,{{cos }^2},eta , + ,,2,cos ,,alpha ,,cos ,eta ,cos ,,(eta - alpha ),}}$$
$${{pi ,{d^2},,{{cos }^2},,alpha } over {{{sin }^2},alpha , + ,{{cos }^2},eta , + ,,2,cos ,,alpha ,,cos ,eta ,cos ,,(eta - alpha ),}}$$
$${{pi ,{d^2},,{{cos }^2},,alpha } over {{{cos }^2},alpha , + ,{{cos }^2},eta , - ,,2,cos ,,alpha ,,cos ,eta ,cos ,,(eta - alpha ),}}$$
$${{pi ,{d^2},,{{cos }^2},,eta } over {{{cos }^2},alpha , + ,{{cos }^2},eta , + ,,2,cos ,,alpha ,,cos ,eta ,cos ,,(eta - alpha ),}}$$
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