Tag: construction related to lines

Questions Related to construction related to lines

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) $

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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 $(8, - 5)$

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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.

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

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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. $4m$

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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 } $

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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 $6\left ( \dfrac {\sqrt{3}}{4}a^{2} \right )=6*\dfrac {\sqrt{3}}{4}\dfrac {20\sqrt{3}}{3}\dfrac {20\sqrt{3}}{3}=200\sqrt{3}$

With the help of a normal ruler and a compass only, which of the following line segment is possible to construct?

maths line segment construction of line segment and circle of given radius construction related to lines constructing line segment circumscribing and inscribing a circle on a regular hexagon

  1. $2.1\ cm$

  2. $4.2\ cm$

  3. $5.43\ cm$

  4. $3.3\ cm$

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Correct Option: A,B,D
Explanation:

Least count of normal scale is $.1\ \ cm$ that is minimum length that can be measured using a normal scale is $.1\ \ cm$.

So the lengths that can be measured are
$2.1\ \ cm,4.2\ \ cm$ and $3.3\ \ cm$
To measure $5.43$ we need a scale whose least count is $.001$

Which of the following line segments can be drawn with the help of a ruler and compass ?

maths line segment construction of line segment and circle of given radius construction related to lines constructing line segment circumscribing and inscribing a circle on a regular hexagon

  1. $1.234\ cm$

  2. $2.15\ cm$

  3. $2.5\ cm$

  4. $3.04\ cm$

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Correct Option: C
Explanation:

Least count of normal scale is $.1\ \ cm$ that is minimum length that can be measured using a normal scale is $.1\ \ cm$

So only $2.5 \ \ cm$ can be measured using a ruler and compass.
Hence option $C$ is correct.

With the help of a normal ruler, which of the following line segment is possible to construct?

maths line segment construction of line segment and circle of given radius construction related to lines constructing line segment circumscribing and inscribing a circle on a regular hexagon

  1. $3.1\ cm$

  2. $4.234\ cm$

  3. $7.2\ cm$

  4. $1\ cm $

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Correct Option: A,C,D
Explanation:

Least count of normal scale is $.1\ \ cm$ that is minimum length that can be measured using a normal scale is $.1\ \ cm$

So the lengths that can be measures are
$3.1\ \ cm$$,7.2\ \ cm$ and $1cm\ \ $
Options $A,C$ and $D$ are correct.

The steps for constructing a line segment of given length are given in a jumbled order below:
1. Draw an arc on the line by keeping the pointed end of the compass on the point $A$. Mark the arc point as $B$.
2. Draw a line.
3. Extend the compass by keeping one end on the $0\ cm$ mark and other at the given length on the ruler.
4. Take a point $A$ anywhere on the line.

Which of the above steps comes last?

maths line segment construction of line segment and circle of given radius construction related to lines constructing line segment circumscribing and inscribing a circle on a regular hexagon

  1. $1$

  2. $2$

  3. $3$

  4. $4$

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Correct Option: A
Explanation:

For constructing a line segment of given length steps are following:

Step 1 : Draw a line(2).
Step 2 :Take a point $A$ anywhere on the line(4).
Step 3 : Extend the compass by keeping one end on the $0 \ \ cm$ mark and other at given length on ruler(3).
Step 4 :  Draw an arc on the line by keeping the pointed end of the compass on the point $A$ .Mark the arc point as $B.$(1)
So $1.$ is the last step.
Option $A$ is correct.