Partitioned Areas

Geometry Level 2

A right triangle ABCABC is divided into six smaller triangles by lines drawn from the vertices through a common interior point named as OO.

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

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

What is the area of triangle ABCABC?


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