I Dare You To Take A Special Case! Part 2

Geometry Level 5

Let \(\Gamma_1\) be the circumcircle of \(\Delta ABC\) and \(\Gamma_2\) be the circumcircle of \(\Delta DEF\) where \(D,E,F\) are the foot of the altitudes of \(\Delta ABC\).

If \(\Gamma_1\) cuts \(\Gamma_2\) orthogonally, compute the value of the following expression upto three decimal places:

\[ \sum_\text{cyc} \cos 2A \]


  • \(A\) denotes \(\angle BAC\). \(B\) and \(C\) are defined similarly.
  • \(\displaystyle \sum_\text{cyc}\) denotes cyclic summation.

This problem is part of my set: Geometry

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