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2004 AMC 10BProblem 24P21-25~5 minPrint
CirclesSimilar & Congruent TrianglesTriangle Centers & CeviansAdd construction lines/points (drop altitudes, extend segments, connect centers)Set up the equation/formula and compute; no special trick needed

In triangle ABCABC we have AB=7AB=7 , AC=8AC=8 , BC=9BC=9 . Point DD is on the circumscribed circle of the triangle so that ADAD bisects angle BACBAC . What is the value of ADCD\frac{AD}{CD} ?

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Problem © Mathematical Association of America (MAA), American Mathematics Competitions. Reproduced for non-commercial educational use. Solution and commentary are original to this site.