FERMAT 2021 Problem 18

In the diagram, \triangle P Q R is an isosceles triangle with P Q=P R. Semi-circles with diameters P Q, Q R and P R are drawn. The sum of the areas of these three semicircles is equal to 5 times the area of the semi-circle with diameter Q R. The value of \cos (\angle P Q R) is

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Answer Choices
A. \frac{1}{3}
B. \frac{1}{\sqrt{8}}
C. \frac{1}{\sqrt{12}}
D. \frac{1}{\sqrt{15}}
E. \frac{1}{\sqrt{10}}