2021 China's Math Olympiad – Q8: Geometric Interpretation to the rescue. An optimization problem

2021 China’s Math Olympiad – Question 8(fill-in-the-blank)

x,y∈R + satisfies: There exists a, b, a∈[0,x], b∈[0,y], such that

a^2+y^2=2, b^2+x^2=1, ax+by=1

What is the max of x+yx+y?

00:00:00 Introduction: Problem Statement
00:00:40 A possible approach, but leads to complex algebraic equations
00:02:40 Geometric interpretation is useful in solving the problem
00:06:14 Use the geometric setup to formulate the problem
00:07:08 Use algebra to solve the problem under the previous setup
00:11:20 Summary

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