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KöMaL 2013 B4507

    The area of a regular heptagon is 4095 units. AA and BB are two consecutive vertices, and KK is the centre of the heptagon. PP is a point lying on the circumscribed circle of triangle ABK in the interior of the heptagon. Given that AP−PBAB=23\frac{AP-PB}{AB}=\frac{2}{3}, what may be the area of triangle ABP ?

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