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Ratio of Lines in a Triangle

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January 15, 2009
ratiocircumcirclegeometryangle bisectorpower of a point

Problem Statement

In △ABC \triangle ABC we have AB \equal{} 7, AC \equal{} 8, and BC \equal{} 9. Point D D is on the circumscribed circle of the triangle so that AD‾ \overline{AD} bisects ∠BAC \angle BAC. What is the value of AD/CD AD/CD? <spanclass=′latex−bold′>(A)</span> 98<spanclass=′latex−bold′>(B)</span> 53<spanclass=′latex−bold′>(C)</span> 2<spanclass=′latex−bold′>(D)</span> 177<spanclass=′latex−bold′>(E)</span> 52 <span class='latex-bold'>(A)</span>\ \frac{9}{8}\qquad <span class='latex-bold'>(B)</span>\ \frac{5}{3}\qquad <span class='latex-bold'>(C)</span>\ 2\qquad <span class='latex-bold'>(D)</span>\ \frac{17}{7}\qquad <span class='latex-bold'>(E)</span>\ \frac{5}{2}
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