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SMT RMT 2014 Geometry Tiebreaker #3

Source:

October 28, 2022
geometry

Problem Statement

Circle OO has three chords, ADAD, DFDF, and EFEF. Point E lies along the arc ADAD. Point CC is the intersection of chords ADAD and EFEF. Point BB lies on segment ACAC such that EB=EC=8EB = EC = 8. Given AB=6AB = 6, BC=10BC = 10, and CD=9CD = 9, find DFDF. https://cdn.artofproblemsolving.com/attachments/f/c/c36bff9ad04f13f7e227c57bddb53a0bfc0569.png
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