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Question Number 145244 by gsk2684 last updated on 03/Jul/21

$$\mathrm{consider}\mathrm{the}\mathrm{circle}$$$${(\mathrm{x}-1)}^2+{(\mathrm{y}-1)}^2=2,$$$$\mathrm{A}(1,4),\mathrm{B}(1,-5).\mathrm{if}\mathrm{P}\mathrm{is}$$$$\mathrm{a}\mathrm{point}\mathrm{on}\mathrm{the}\mathrm{circle}\mathrm{such}\mathrm{that}$$$$\mathrm{PA}+\mathrm{PB}\mathrm{is}\mathrm{maximum}\mathrm{then}$$$$\mathrm{prove}\mathrm{that}\mathrm{P},\mathrm{A},\mathrm{B}\mathrm{are}\mathrm{collinear}$$$$\mathrm{points}.$$

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