Computational Geometry
AwesomeMath Summer Program 2025
Computational Geometry
Last update: May 27, 2025
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Geometric Inequalities
Problem 1: Prove that for any triangle ABC with sides a, b and c the following inequality holds
a
b
c
+
+
≥ 3.
b+c−a
c+a−b
a+b−c
eM
at
1
AB + AD + BC ≥ CD.
2
h
Problem 2: In convex quadrilateral ABCD let M be the midpoint of AB. Assume that ∠CM D = 120◦ . Prove that
Aw
es
om
Problem 3: Prove that of all triangles with a given area, the equilateral triangle has the shortest perimeter.
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