Answer:
Step-by-step explanation:
it is given that Square contains a chord of of the circle equal to the radius thus from diagram
[tex]QR=chord =radius =R[/tex]
If Chord is equal to radius then triangle PQR is an equilateral Triangle
Thus [tex]QO=\frac{R}{2}=RO[/tex]
In triangle PQO applying Pythagoras theorem
[tex](PQ)^2=(PO)^2+(QO)^2[/tex]
[tex]PO=\sqrt{(PQ)^2-(QO)^2}[/tex]
[tex]PO=\sqrt{R^2-\frac{R^2}{4}}[/tex]
[tex]PO=\frac{\sqrt{3}}{2}R[/tex]
Thus length of Side of square [tex]=2PO=\sqrt{3}R[/tex]
Area of square[tex]=(\sqrt{3}R)^2=3R^2[/tex]
Area of Circle[tex]=\pi R^2[/tex]
Ratio of square to the circle[tex]=\frac{3R^2}{\pi R^2}=\frac{3}{\pi }[/tex]
