Advanced Geometric Problem & Solution (Twice a week update) Now 4639 problems posted.
<Tri-2025-2195>, hint
(a+b)^2=(2+c)^2 2ab= 4+c^2
Consider A-G mean inequality (2+c)>=2(2+c^2/2)^ (1/2)
(c-2)^2 <=0, Hence c=2
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