Partitioned Areas

Geometry Level 3

A right triangle \(ABC\) is divided into six smaller triangles by lines drawn from the vertices through a common interior point named as \(O\).

These lines which are drawn from vertices \(A,B,C\) meet \(BC,AC,AB\) at points \( D,E,F\), respectively.

The areas of triangles \(AFO, OEC, ODC, OBD\) are 84,35,30 and 40, respectively.

What is the area of triangle \(ABC\)?

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