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The Extouch and Intouch Triangles of a Triangle

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.
The extouch triangle of a triangle is formed by the three points where the excircles are tangent to the triangle's sides.
The intouch triangle of a triangle is formed by the three points where the incircle is tangent to the triangle's sides. (The intouch triangle is also known as the contact triangle.)
The areas of the extouch and intouch triangles of a triangle are equal.

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The statement of the theorem is in Problem 86. Intouch and Extouch Triangles, Area.
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