Tag: constructions related to a circle

Questions Related to constructions related to a circle

The centre of the circle circumscribing the square whose three sides are $3x+y=22,x-3y=14$ and $3x=y=62$ is:

maths construction circumscribing and inscribing a circle on a regular hexagon constructions related to a circle construction of polygons construction of tangent to a circle construction of tangents construction of line segment and circle of given radius construction related to lines

  1. $\left( \dfrac { 3 }{ 2 } ,\dfrac { 27 }{ 2 } \right) $

  2. $\left( \dfrac { 27 }{ 2 } ,\dfrac { 3 }{ 2 } \right) $

  3. $(27,3)$

  4. $\left( 1,\dfrac { 2 }{ 3 } \right) $

Show answer
Correct Option: B

A square is inscribed in the circle $x^2 + y^2 -2x +4y - 93 = 0$ with its sides parallel to the coordinates axes. The coordinates of its vertices are 

maths construction circumscribing and inscribing a circle on a regular hexagon constructions related to a circle construction of polygons construction of tangent to a circle construction of tangents construction of line segment and circle of given radius construction related to lines

  1. $( - 6, - 9), \, ( - 6, 5), \, (8, - 9)$ and $(8, 5)$

  2. $( - 6, 9), \, ( - 6, - 5), \, (8, - 9)$ and $(8, 5)$

  3. $( - 6, - 9), \, ( - 6, 5), \, (8, 9)$ and $(8, 5)$

  4. $( - 6, - 9), \, ( - 6, 5), \, (8, - 9)$ and $(8, - 5)$

Show answer
Correct Option: A

For each of the following, drawn a circle and inscribe the figure given.If a polygon of the given type can't be inscribed,write not possible.

maths construction circumscribing and inscribing a circle on a regular hexagon constructions related to a circle construction of polygons construction of tangent to a circle construction of tangents construction of line segment and circle of given radius construction related to lines

  1. Rectangle.

  2. Trapezium.

  3. Obtuse triangle.

  4. non-rectangle parallelogram

  5. Accute isosceles triangle.

  6. A quadrilateral PQRS with $\overline {PR} $ as diameter.

Show answer
Correct Option: A

In regular hexagon, if the radius of circle through vertices is r, then length of the side will be

maths construction circumscribing and inscribing a circle on a regular hexagon constructions related to a circle construction of polygons construction of tangent to a circle construction of tangents construction of line segment and circle of given radius construction related to lines

  1. $\displaystyle \frac{2\pi r}{6}$

  2. r

  3. $\displaystyle \frac{\pi r}{6}$

  4. $\displaystyle \frac{r}{2}$

Show answer
Correct Option: B
Explanation:

$\Rightarrow$   Radius of a circle is $r$.

$\Rightarrow$   In regular hexagon all sides are equal.
$\Rightarrow$   The regular hexagon has 6 equilateral triangles. The diameter of the circle is $2r$ in this case, will coincide with 2 equilateral triangles. So the side of the hexagon will be $r$.
$\therefore$   Length of side of hexagon is $r$.

When constructing the circles circumscribing and inscribing a regular hexagon with radius $3$ m, then inscribing hexagon length of each side is

maths construction circumscribing and inscribing a circle on a regular hexagon constructions related to a circle construction of polygons construction of tangent to a circle construction of tangents construction of line segment and circle of given radius construction related to lines

  1. $1m$

  2. $2m$

  3. $3m$

  4. $4m$

Show answer
Correct Option: C
Explanation:

When constructing the circles circumscribing and inscribing a regular hexagon with radius $3$ m, then inscribing hexagon length of each side is $3$ m.

The area of a circle inscribed in a regular hexagon is $100\pi$. The area of the hexagon is:

maths construction circumscribing and inscribing a circle on a regular hexagon constructions related to a circle construction of polygons construction of tangent to a circle construction of tangents construction of line segment and circle of given radius construction related to lines

  1. $600$

  2. $300$

  3. $200\sqrt { 2 } $

  4. $200\sqrt { 3 } $

  5. $200\sqrt { 5 } $

Show answer
Correct Option: D
Explanation:

Area of circle $=100\pi $
$\pi r^{2}=100\pi $
$r^{2}=100$
$r=10$
Now, a regular hexagon is made up of 6 equilateral $\bigtriangleup s $ of equal areas. Now, height of equilateral $\bigtriangleup  $ is equal to radius of circle.Therefore, ar. of 1 equilateral $\bigtriangleup=\dfrac {1}{2} $ x base x height
$\Rightarrow \dfrac {\sqrt{3}}{4}a^{2}=\dfrac {1}{2}a*10\Rightarrow a=\dfrac {4*10}{2\sqrt{3}}=\dfrac {20\sqrt{3}}{3} $
Area of hexagon $6\left ( \dfrac {\sqrt{3}}{4}a^{2} \right )=6*\dfrac {\sqrt{3}}{4}\dfrac {20\sqrt{3}}{3}\dfrac {20\sqrt{3}}{3}=200\sqrt{3}$