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2012 preRMO p20, area of the region bounded by 2 semicircular arcs

Source:

June 17, 2019

geometryareafunky circlessemicircle

Problem Statement

PXS

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?

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