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Incircle touch points angle

High school · ●●○○○ 20 pts

In triangle ABCABC, ∠BAC=72∘\angle BAC = 72^\circ. The incircle of triangle ABCABC touches sides BCBC, ACAC, and ABAB at DD, EE, and FF, respectively. Find ∠EDF\angle EDF, in degrees.

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incircletangent lengthsisosceles triangles