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2005 AMC 10BProblem 10P1-10~3 minPrint
Triangles: Area & PythagoreanAdd construction lines/points (drop altitudes, extend segments, connect centers)Set up the equation/formula and compute; no special trick needed

In △ABC\triangle ABC , we have AC=BC=7AC=BC=7 and AB=2AB=2 . Suppose that DD is a point on line ABAB such that BB lies between AA and DD and CD=8CD=8 . What is BDBD ?

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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. Also appeared as 2005 12B #6.