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rectangle inscribed in triangle 2021-22 Dürer Round1 C4 D3

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December 1, 2022
geometryrectangleDurer

Problem Statement

We inscribed in triangle ABCABC the rectangle DEFGDEFG such that DD and EE fall on side ABAB, FF on side BCBC, and GG on side ACAC. We know that AFAF bisects angle ∠BAC\angle BAC, and that ADDE=12\frac{AD}{DE} = \frac12. What is the measure of angle ∠CAB\angle CAB?
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