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Geometry Level 3

The right-angled triangle \(ABC\) has area \(2016\text{ cm}^2\).

Lines \(AI, IF, IE, EH, HD\) and \(DG \) divide the large triangle into seven smaller triangles of equal area.

IF triangle \(BIE\) is an isosceles triangle, find the length of \(BG\) in centimetres.

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