What If I take \(a^2+b^2+c^2=11\) out

Geometry Level pending

Consider triangle \(ABC\), such that:

  1. \(\angle A = 45^\circ\)

  2. \(\tan A, \tan B, \tan C\) are in an arithmetic progression.

Find \(\dfrac{{CH}^2}{\triangle}\) to 4 decimal places, where \(H\) is the orthocenter and \(\triangle\) is the area of triangle \(ABC\).

Inspiration

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