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Point inside Isosceles right triangle

Source: LIMIT 2020 Cat 2 Obj P11

May 25, 2020
limitgeometry

Problem Statement

△PQR\triangle PQR is isosceles and right angled at RR. Point AA is inside △PQR\triangle PQR, such that PA=11,QA=7PA=11, QA=7, and RA=6RA=6. Legs PR‾\overline{PR} and QR‾\overline{QR} have length s=a+b2s=\sqrt{a+b\sqrt{2}}, where aa and bb are positive integers. What is a+ba+b?
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