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Area of an Obtuse triangle from Equilateral triangle (Posted on 2023-09-08) Difficulty: 3 of 5
In Obtuse triangle from equilateral triangle we were asked to construct an 120-degree obtuse triangle from segments of an equilateral triangle ABC and an arbitrary cevian BD.

What is the area of this 120-degree obtuse triangle expressed in terms of the lengths of side AB and cevian BD?

No Solution Yet Submitted by Brian Smith    
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Solution Solution Comment 1 of 1
Using your geometric solution to name the extra points (which is essentially how I solved this problem when I came across it.)

[DFC] = 2*[ABC] - [ABD] - [DBF] - [FBE]

triangle FBE is congruent to triangle DBC, so [ABD]+[FBE]=[ABC]

[DFC] = [ABC] - [DBF]

these are both equilateral so the area is simply

[DFC] = sqrt(3)/4 ((AB)^2-(BD)^2)


  Posted by Jer on 2023-09-09 11:40:22
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