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Triangle Incribed in Semicircle

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February 1, 2009
geometryperimeter

Problem Statement

If △ABC \triangle ABC is inscribed in a semicircle whose diameter is AB AB, then AC \plus{} BC must be <spanclass=′latex−bold′>(A)</span> equal to AB<spanclass=′latex−bold′>(B)</span> equal to AB2<spanclass=′latex−bold′>(C)</span> ≥AB2 <span class='latex-bold'>(A)</span>\ \text{equal to }AB \qquad<span class='latex-bold'>(B)</span>\ \text{equal to }AB\sqrt {2} \qquad<span class='latex-bold'>(C)</span>\ \geq AB\sqrt {2} <spanclass=′latex−bold′>(D)</span> ≤AB2<spanclass=′latex−bold′>(E)</span> AB2 <span class='latex-bold'>(D)</span>\ \leq AB\sqrt {2} \qquad<span class='latex-bold'>(E)</span>\ AB^2
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