A Problem from Pre-RMO 2012.

Geometry Level 2

PS is a line segment of length 4 and O is the midpoint of PS . A semicircular arc is drawn with PS as diameter. Let X be the midpoint of this arc. Q and R are points on the arc PXS such that QR is parallel to PS and the semicircular arc drawn with QR as diameter is tangent to PS . What is the area of the region QXROQ bounded by the two semicircular arcs?

2 π − 3 2 \pi - 3 2 π − 4 2 \pi - 4 2 π − 2 2 \pi - 2 2 π − 1 2 \pi - 1

Kunal Joshi by Kunal Joshi , 24, India

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