The　principle　of　evaluating　the　minimum　circumscribed　circle　and　maximum　inscribed　circle　determined　by　an　acute　angle　triangle　has　been　used　for　a　long　time　in　industrial　environment.　However,　this　principle　is　not　full　accurate　through　the　further　research　on　it.　In　order　to　make　the　principle　more　comprehensive,　the　obtuse　angle　triangle　is　proposed　and　regarded　as　the　supplement　of　the　original　principle.　Then　the　error　value　of　the　minimum　circumscribed　circle　and　maximum　inscribed　circle　is　obtained　correctly.　The　validated　result　shows　that　the　proposed　principle　offers　an　effective　way　to　identify　the　critical　data　points　and　gives　an　efficient　approach　to　solve　the　circularity　problems.