Square, Triangle, And Semicircle Living In Harmony

Geometry Level 4

In the figure above:

  • The square \(ABCD\) has area 12.25.

  • \(E\) is the intersection of \(BD\) and the semicircle of diameter \(AD.\)

  • \(CF\) is a segment drawn from \(C\) and tangent to the semicircle at \(F.\)

Calculate the area of the triangle \(DEF.\) Give your answer to three decimal places.

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