Unexpected result from Wolfram|Alpha in optimization with constraints

[chincodelaw (dave john)]

local minima 4x+4y , x^2+y^2 = 680 , x>= 3 , y >= 3 - Wolfram|Alpha

I’m not familiar with extrema of a function more than 1 variable, but I guess concept of Local/Global max/min will be the same

Clearly, f(x,y) = (18.4391, 18.4391) is not the local minimum ( try x =5 , y = 25.593)

Did Wolfram|Alpha give wrong answer or I’m missing something?

Thanks.