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computational in a triangle (Chile 1992 L2 P5)

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May 27, 2019
geometryanglesSides

Problem Statement

In the △ABC\triangle ABC , points M,I,H M, I, H are feet, respectively, of the median, bisector and height, drawn from A A . It is known that BC=2 BC = 2 , MI=2−3 MI = 2-\sqrt {3} and AB>AC AB > AC . a) Prove that I I lies between M M and H H . b) Calculate AB2−AC2 AB ^ 2-AC ^ 2 . c) Determine ABAC \dfrac {AB} {AC} . d) Find the measure of all the sides and angles of the triangle.
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