Perform formal constructions with compass/straightedge, paper folding, string, reflective devices, or geometry software.
Determine whether side lengths can form a constructed triangle
Problem
Analyze the displayed side lengths with the triangle inequality, relate the result to the construction circles' intersections, and determine nondegenerate-triangle feasibility and the number of mirror-image constructions.
Triangle construction can be read as a circle-intersection problem. We’ll compare the longest length with the sum of the other two, translate that strictness into the relationship among center distance and the two radii, and then use the number and symmetry of circle intersections to count possible nondegenerate placements.
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