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In triangle ABC, let O be the excenter and DE be perpendicular to AO. Prove that DE is twice the geometric mean of BD and CE that is \(DE = 2\sqrt{d \cdot e}\).
In triangle's heart,
O, excenter, guides the lines,
DE, twice the mean.
Explore Problem 66 with Interactive Wolfram Demonstration Project
Warendorff, Jay, contributor, after work by Antonio Gutierrez. "Tangents to an Excircle." Wolfram Demonstrations Project, March 2011.
https://demonstrations.wolfram.com/TangentsToAnExcircle/
