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Three horses are grazing within a semi-circular field. In the diagram given below, AB is the diameter of the semi-circular field with center at O. Horses are tied up at P, R and S such that PO and RO are the radii of semi-circles with centres at P and R respectively, and S is the centre of the circle touching the two semicircles with diameter AO and OB. The horses tied at P and R can graze within the respective semi-circles and the horse tied at S can graze within the circles centered at S. The percentage of the area of the semi-circle with diameter AB that cannot be grazed by the horses is nearest to

  1. $20$
  2. $28$
  3. $36$
  4. $40$
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