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2017 G3: Two Differences Determine Another Difference

Source:

January 29, 2017
2017geometry

Problem Statement

In acute triangle ABCABC, points DD and EE are the feet of the angle bisector and altitude from AA respectively. Suppose that AC−AB=36AC - AB = 36 and DC−DB=24DC - DB = 24. Compute EC−EBEC - EB.
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