Is the information sufficient 3?

Geometry Level 4

Given that:

  • \( \overline{AD} \) is the median of \( \triangle \text{ABC} \)
  • \( E \) and \( F \) are 2 points on \( \overline{AD} \) such that, \( \overline{AE} : \overline{EF} : \overline{FD} = 4: 3: 1\)
  • When \( \overline{BE} \) and \( \overline{BF} \) are extended going to \( \overline{AC} \), it will intersect \( \overline{AC} \) at points \( G \) and \( H \) respectively.

If the Area of \( \triangle \text{HDC} \) is \( 224 \ \text{sq. units } \) , then what is the area of \( \triangle \text{ABC} \)?

Don't mind the lower case letters, just mind the bigger case letters.


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