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Harcourt's theorem - Wikipedia

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Harcourt Social Studies Homework and Practice Book Student Edition Grade 4 States and Regions Book D

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Harcourt's theorem

Harcourt's theorem is a formula in geometry for the area of a triangle , as a function of its side lengths and the perpendicular distances of its vertices from an arbitrary line tangent to its incircle. The theorem is named after J. Harcourt, an Irish professor. Let a triangle be given with vertices A , B , and C , opposite sides of lengths a , b , and c , area K , and a line that is tangent to the triangle's incircle at any point on that circle. Denote the signed perpendicular distances of the vertices from the line as a ', b ', and c ', with a distance being negative if and only if the vertex is on the opposite side of the line from the incenter. If the tangent line contains one of the sides of the triangle, then two of the distances are zero and the formula collapses to the familiar formula that twice the area of a triangle is a base the coinciding triangle side times the altitude from that base.

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Houghton Mifflin Harcourt eTextbooks are digital replicas of our award winning textbooks. Now students and educators can access the same great content they've come to expect from Houghton Mifflin Harcourt on iPad - for learning and studying anywhere, anytime. The HMH eTextbooks app allows you to read Houghton Mifflin Harcourt eTextbooks on your tablet device, and even organizes all your titles in one convenient place. Download your free HMH eTextbooks app and start building your mobile library today! Note: HMH eTextbooks cannot be purchased via this app, it is an application for educational institutions to download and view eTextbooks they have purchased and licensed from Houghton Mifflin Harcourt. I have to use this app for school and it is really a bad app to work with. First, you cannot multitask like on other apps with books, which makes working a lot more difficult.

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