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area wanted, incircle related 1989 Kyiv City MO 9.1

Source:

July 17, 2021
geometryareaincircle

Problem Statement

The perimeter of the triangle ABCABC is equal to 2p2p, the length of the sideAC AC is equal to bb, the angle ABCABC is equal to β\beta. A circle with center at point OO, inscribed in this triangle, touches the side BCBC at point KK. Calculate the area of ​​the triangle BOKBOK.
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