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• Geometry
• Circles
• Circles and Hexagons

Circles and Hexagons

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•  Question 1: 1 pts A regular hexagon is inscribed in a circle. If the radius of the circle is $5 cm,$ what is the length of the side of the hexagon?
•  Question 2: 1 pts A regular hexagon is inscribed in a circle. Find the area of the circle shown on the picture.
 $A=16\pi cm^{2}$ $A=32\pi cm^{2}$ $A=64\pi cm^{2}$
•  Question 3: 1 pts A regular hexagon with area $\dfrac{3\sqrt{3}}{2} m^{2}$ is inscribed in a circle. Find the area of the circle.
 $A=2\pi m^{2}$ $A=\pi m^{2}$ $A=4\pi m^{2}$ $A=\dfrac{\pi}{2} m^{2}$
•  Question 4: 1 pts A regular hexagon with a side length $x$ can be inscribed inside a circle of a radius $x$?
•  Question 5: 2 pts The area of a circle inscribed in a regular hexagon is $3\pi cm^{2}$. Find the area of described circle of that hexagon.
 $A=2\pi cm^{2}$ $A=\pi cm^{2}$ $A=4\pi cm^{2}$
•  Question 6: 2 pts The perimeter of the shaded figure shown on the picture is $$P=48\pi cm.$$
•  Question 7: 2 pts Which expression can be used to find the area of a circle inscribed in a regular hexagon with a perimeter of $48cm$?
 $A={\left(4\sqrt{2}\right)^{2}}\pi =32\pi cm^{2}$ $A={\left(4\sqrt{3}\right)^{2}}\pi =48\pi cm^{2}$ $A={\left(8\sqrt{6}\right)^{2}}\pi =384\pi cm^{2}$ $A={\left(2\sqrt{3}\right)^{2}}\pi =14\pi cm^{2}$
•  Question 8: 2 pts If a regular hexagon is inscribed in a circle with a radius of $4 cm$, find the area of the hexagon.
 $A=24\sqrt{2} cm^{2}$ $A=18\sqrt{3}\pi cm^{2}$ $A=24\sqrt{3}\pi cm^{2}$ $A=16\sqrt{3}\pi cm^{2}$
•  Question 9: 2 pts A circle is inscribed in a regular hexagon. A regular hexagon is inscribed in this circle. Another circle is inscribed in the inner regular hexagon and so on. What is the area of the third such circle if the length of the side of the outermost regular hexagon is 8 cm.
 $A=3\pi cm^{2}$ $A=9\pi cm^{2}$ $A=27\pi cm^{2}$ $A=36\pi cm^{2}$
•  Question 10: 3 pts In a circle of radius $3$ the equilateral triangle $ABC$ is inscribed, and the points $X, Y$ and $Z$ are diametrically opposite to $A, B$ and $C$ (respect) . Find the perimeter of the hexagon $AZBXCY.$
$A=$
•  Question 11: 3 pts A circle is inscribed within a regular hexagon in such a way that the circle touches all sides of the hexagon at exactly one point per side. Another circle is drawn to connect all the vertices of the hexagon. Expressed as a fraction, what is the ratio of the area of the smaller circle to the area of the larger circle?
 $3:4$ $\sqrt{3}:3$ $3:\sqrt{2}$ $4:3$
•  Question 12: 3 pts A regular hexagon of a side $12cm$ is inscribed in a circle. Another circle is in turn inscribed in the hexagon. What is the area of the region between the 2 circles?