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Sum of squares of lengths in a triangle

Source: South African MO 2010 Q2

May 26, 2012
trigonometrygeometry unsolvedgeometry

Problem Statement

Consider a triangle ABCABC with BC=3BC = 3. Choose a point DD on BCBC such that BD=2BD = 2. Find the value of AB2+2AC2āˆ’3AD2.AB^2 + 2AC^2 - 3AD^2.
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