2011 AMC 12A Problems/Problem 25

Problem

Triangle $ABC$ has $\angle BAC = 60^\{\circ}$ (Error compiling LaTeX. Unknown error_msg), $\angle CBA \leq 90^\{\circ}$ (Error compiling LaTeX. Unknown error_msg), $BC=1$ , and $AC \geq AB$ . Let $H$ , $I$ , and $O$ be the orthocenter, incenter, and circumcenter of $\triangle ABC$ , repsectively. Assume that the area of pentagon $BCOIH$ is the maximum possible. What is $\angle CBA$ ?

$\textbf{(A)}\ 60^{\circ} \qquad \textbf{(B)}\ 72^{\circ} \qquad \textbf{(C)}\ 75^{\circ} \qquad \textbf{(D)}\ 80^{\circ} \qquad \textbf{(E)}\ 90^{\circ}$

Solution

2011 AMC 12A (Problems • Answer Key • Resources)
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2011 AMC 12A Problems/Problem 25

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