# Partitioned Areas

Geometry Level 2

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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