Tangents to an Excircle

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A circle drawn outside a triangle that is tangent to the extensions of two of its sides and to the third side is an excircle.

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Let ABC be a triangle. Construct the excircle with center O opposite A. Let D and E be the points of intersection between the line perpendicular to AO and the extensions of AB and AC. Then .

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Contributed by: Jay Warendorff (March 2011)
After work by: Antonio Gutierrez
Open content licensed under CC BY-NC-SA


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The statement of the theorem is in Problem 66. Triangle, Excircle, Tangents, Geometric Mean.



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