A Triangle from Perimeter and Inradius

★ 7/10plane geometry trigonometry Law of Cosines Substitution Triangle Geometry

Problem

A triangle $ABC$ has perimeter $12$ and inradius $1$ . Determine, with proof, whether $\triangle ABC$ must be right-angled, must be acute, must be right or acute, or none of these.

Answer

Solution

Difficulty	7/10
Topics	plane geometry, trigonometry, Law of Cosines, Substitution, Triangle Geometry

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