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GradeCircumscribing and inscribing a circle on Regular Hexagon

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What is the area of a regular hexagon inscribed in a circle of radius r ? \[\]

A. $ 2\sqrt{3}{{r}^{2}}\text{ sq}\text{.units } $ \[\]

B. $ \dfrac{3\sqrt{3}}{2}{{r}^{2}}\text{ sq}\text{.units } $ \[\]

C. $ \dfrac{2}{\sqrt{3}}{{r}^{2}}\text{ sq}\text{.units } $ \[\]

D. $ \dfrac{\sqrt{3}}{2}{{r}^{2}}\text{ sq}\text{.units } $ \[\]

A. $ 2\sqrt{3}{{r}^{2}}\text{ sq}\text{.units } $ \[\]

B. $ \dfrac{3\sqrt{3}}{2}{{r}^{2}}\text{ sq}\text{.units } $ \[\]

C. $ \dfrac{2}{\sqrt{3}}{{r}^{2}}\text{ sq}\text{.units } $ \[\]

D. $ \dfrac{\sqrt{3}}{2}{{r}^{2}}\text{ sq}\text{.units } $ \[\]

If a hexagon $ABCDEF$ circumscribes a circle. Prove that $AB + CD + EF = BC + DE + FA$.

If a hexagon ABCDEF circumscribe a circle, prove that \[\text{AB}+\text{CD}+\text{EF}=\text{BC}+\text{DE}+\text{FA}\].

The side of a regular hexagon is 2cm. Then the ratio of the radius of the circumscribed circle to the radius of the inscribed circle is?

A. $\dfrac{{\sqrt 3 }}{2}$

B. $\dfrac{1}{2}$

C. $2$

D. $\dfrac{2}{{\sqrt 3 }}$

A. $\dfrac{{\sqrt 3 }}{2}$

B. $\dfrac{1}{2}$

C. $2$

D. $\dfrac{2}{{\sqrt 3 }}$

When constructing an inscribed regular hexagon, how will you choose the arc measurement?

(a) Radius of the circle

(b) Diameter of the circle

(c) Chord of the circle

(d) Circumference of the circle

(a) Radius of the circle

(b) Diameter of the circle

(c) Chord of the circle

(d) Circumference of the circle

A regular hexagon is inscribed in a circle of radius \[r\]. The perimeter of regular hexagon is

A. \[3r\]

B. \[6r\]

C. \[9r\]

D. \[12r\]

A. \[3r\]

B. \[6r\]

C. \[9r\]

D. \[12r\]

ABCDEF is a regular hexagon with center O. If the area of the triangle OAB is 9 $cm^2$, find the area of the circle in which the hexagon is inscribed.

Construct a regular hexagon of side $5 cm$. Hence determine the number of lines of symmetry can be drawn for a regular hexagon.

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