<s>[INST] in a triangle $ABC,$ if $2c^2=a^2+b^2,$ then largest possible degree measure of angle $C$ is In a triangle $ABC,$ if $2c^2=a^2+b^2,$ then largest possible degree measure of angle $C$ is 
cosine formula $\displaystyle \cos C = \frac{a^2+b^2-c^2}{2ab} = \frac{c^2}{2ab}<\frac{(a+b)^2}{2ab}=\frac{a^2+b^2}{2ab}+1$
wan,t be able to process after that, could some help me
 [/INST] $$\cos{C}=\dfrac{a^2+b^2-c^2}{2ab}=\dfrac{a^2+b^2}{4ab}\ge\dfrac{1}{2}$$
so
$$C\le \dfrac{\pi}{3}$$
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