It's not a pedal triangle!

Geometry Level 4

In the figure given above (for illustration purposes only), points \(A_1\), \((B_1, B_2)\), \((C_1, C_2, C_3)\) are taken on sides \(BC\), \(CA\) and \(AB\) of \(\Delta ABC\) respectively such that

  • \(A_1\) is the mid-point of \(BC\) ;
  • \(B_1\) and \(B_2\) are the points of trisection of \(CA\) ;
  • \(C_1\), \(C_2\) and \(C_3\) divide the segment \(AB\) into four equal parts

A triangle \(\Delta A_1 B_1 C_2\) is constructed with vertices at \(A_1\), \(B_1\) and \(C_2\).

Find \(\dfrac{\text{Area } \Delta ABC}{\text{Area } \Delta A_1 B_1 C_2}\).


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