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2005 Geometry #9: Circle and Point Mumbo Jumbo

Source:

May 16, 2013
geometryanalytic geometrygraphing linesslope

Problem Statement

Let ACAC be a diameter of a circle ω \omega of radius 11, and let DD be a point on ACAC such that CD=15CD=\frac{1}{5}. Let BB be the point on ω\omega such that DBDB is perpendicular to ACAC, and EE is the midpoint of DBDB. The line tangent to ω\omega at BB intersects line CECE at the point XX. Compute AXAX.
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