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25-26-27 Triangle and Its Angle Bisectors

Source: 2012 AMC 12A Problem #18

February 8, 2012
geometryinradiusanalytic geometryarea of a triangleHeron's formulaPythagorean TheoremAMC

Problem Statement

Triangle ABCABC has AB=27AB=27, AC=26AC=26, and BC=25BC=25. Let II denote the intersection of the internal angle bisectors of △ABC\triangle ABC. What is BIBI?
<spanclass=′latex−bold′>(A)</span> 15<spanclass=′latex−bold′>(B)</span> 5+26+33<spanclass=′latex−bold′>(C)</span> 326<spanclass=′latex−bold′>(D)</span> 23546<spanclass=′latex−bold′>(E)</span> 93 <span class='latex-bold'>(A)</span>\ 15\qquad<span class='latex-bold'>(B)</span>\ 5+\sqrt{26}+3\sqrt{3}\qquad<span class='latex-bold'>(C)</span>\ 3\sqrt{26}\qquad<span class='latex-bold'>(D)</span>\ \frac{2}{3}\sqrt{546}\qquad<span class='latex-bold'>(E)</span>\ 9\sqrt{3}
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