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Square on a Triangle

Source:

February 15, 2009

Problem Statement

In triangle ABC ABC, \overline{CA} \equal{} \overline{CB}. On CB CB square BCDE BCDE is constructed away from the triangle. If x x is the number of degrees in angle DAB DAB, then <spanclass=′latex−bold′>(A)</span> x depends upon triangle ABC<spanclass=′latex−bold′>(B)</span> x is independent of the triangle <span class='latex-bold'>(A)</span>\ x\text{ depends upon triangle }ABC \qquad<span class='latex-bold'>(B)</span>\ x\text{ is independent of the triangle} <spanclass=′latex−bold′>(C)</span> x may equal angle CAD<spanclass=′latex−bold′>(D)</span> x can never equal angle CAB <span class='latex-bold'>(C)</span>\ x\text{ may equal angle }CAD \qquad<span class='latex-bold'>(D)</span>\ x\text{ can never equal angle }CAB <spanclass=′latex−bold′>(E)</span> x is greater than 45∘ but less than 90∘ <span class='latex-bold'>(E)</span>\ x\text{ is greater than }45^{\circ}\text{ but less than }90^{\circ}
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