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2 squares and 1 circle - Malaysia 2010 OMK Muda / Intermediate p4

Source:

October 26, 2021
geometry

Problem Statement

A square ABCDABCD has side length 1 1. A circle passes through the vertices of the square. Let P,Q,R,SP, Q, R, S be the midpoints of the arcs which are symmetrical to the arcs ABAB, BCBC, CDCD, DADA when reflected on sides ABAB, BBC, CDCD, DADA, respectively. The area of square PQRSPQRS is a+b2a+b\sqrt2, where aa and b b are integers. Find the value of a+ba+b. https://cdn.artofproblemsolving.com/attachments/4/3/fc9e1bd71b26cfd9ff076db7aa0a396ae64e72.png
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