Geometry Problem 66. Tangents to an Excircle, Geometric Mean. Level: High School, SAT Prep, College

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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 \(DE = 2\sqrt{d \cdot e}\).

Proposed geometry problem 66. Triangle, excircle, geometric mean

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/

Flyer of Problem 66 using iPad Apps

Flyer of problem 66 using iPad App