Tag: circumscribing and inscribing a circle on a regular hexagon

Questions Related to circumscribing and inscribing a circle on a regular hexagon

Construct a line segment of length $4.6\ cm$. Divide this line into $2$ equal parts and find the length of each part.

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. $2.0\ cm$

  2. $2.1\ cm$

  3. $2.2\ cm$

  4. $2.3\ cm$

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Correct Option: D
Explanation:
steps of construction :
1 . draw a line of length 4.6 cm using ruler .
2. Place the compass at one end of line segment.
3 . Adjust the compass to slightly longer than half the line segment length.
4. Draw arcs above and below the line.
 5 .Keeping the same compass width, draw arcs from other end of line.
6 . Place ruler where the arcs cross, and draw the line segment.
7. drawn line segment cuts the initial line segment  into two equal parts .
8. measure the bisected length using ruler thats comes out be $= \dfrac{1}{2} \times 4.6 = 2.3 cm$

Draw a line $AB=7.8\ cm$, what will be the $\dfrac{2}{3}$rd of $AB$.

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. $11.7\ cm$

  2. $5.2\ cm$

  3. $3.9\ cm$

  4. $2.6\ cm$

Show answer
Correct Option: B
Explanation:

Draw a line segment $AB$ of $7.8\ \ cm$ using ruler 

.$\dfrac{2}{3}AB=$ $=\dfrac { 2 }{ 3 } \times 7.8=5.2 \ cm$
Option $B$ is correct.

Construct a line $AB=6.5\ cm$. What will be the $\dfrac{1}{5}$th of $AB$ ?

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. $4.2\ cm$

  2. $3.5\ cm$

  3. $2.4\ cm$

  4. $1.3\ cm$

Show answer
Correct Option: D
Explanation:

Draw a line segment $AB$ of length $6.5\ \ cm$

$\dfrac { 1 }{ 5 } AB=\dfrac { 1 }{ 5 } \times 6.5=1.3\ \ cm$
So option $D$ is correct.

Draw a line $XY=13.6\ cm$. what will be the $\dfrac{1}{4}$th of $XY$ ?

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. $6.8\ cm$

  2. $5.2\ cm$

  3. $3.4\ cm$

  4. $2.2\ cm$

Show answer
Correct Option: C
Explanation:

Draw a line segment $XY$ of length $13.6\ \ cm$

$\dfrac { 1 }{ 4 } XY=\dfrac { 1 }{ 4 } \times 13.6=3.4\ \ cm$
Option $C$ is correct.

Draw a line $PQ=9.6\ cm$. What will be the $\dfrac{1}{3}$rd of $PQ$ ?

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. $3.2\ cm$

  2. $4.6\ cm$

  3. $2.4\ cm$

  4. $2.5\ cm$

Show answer
Correct Option: A
Explanation:

Draw a line segment $PQ$ is length $9.6\ \ cm$ using a ruler.

$\dfrac { 1 }{ 3 } PQ=\dfrac { 1 }{ 3 } \times 9.6=3.2\ \ cm$
So option $A$ is correct.

Use your compasses to draw a circle of radius as specified below. What is the diameter of each of these circles.

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. $5\ cm$

  2. $4\ cm$

  3. $12\ cm$

  4. $7\ cm$

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Correct Option: A

Steps of constructing a line segment equal to the length of given segment is written in jumbled form below:
1. Draw a line $l$. Mark a point $A$ on line $l$. Without changing compass's setting, place the compass at $A$.
2. Make an arc on the line $l$ which cuts $l$ at $B$. Now, $AB$ is a copy of $CD$.
3. Draw a line segment $CD$ of any length.
4. Fix the compass's end on $C$ and pencil on $D$. This gives the length of $CD$.

Which of the above comes first.

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. $4$

Show answer
Correct Option: C
Explanation:

Correct sequence is :

Step 1. Draw a line segment $CD$ of any length.
Step 2 .Fix the compass's end on $C$ and a pencil on $D$. This gives length $CD.$
Step 3. Draw a line $l$. Mark a point $A$ on line $l$.Without changing compass's setting place the compass at $A$
Step 4. Make an arc on the line $l$ whcih cuts $l$ at $B$  Now $AB$ is a copy of $CD$
So the first step is $3$
Option $C$ is correct.

Choose the correct answer from the alternatives given.
Water is flowing at the rate of $5$ km/hr through a pipe of diameter $14$ cm into a rectangular tank which is $50$ m long, $44$ m wide. The time taken (in hours) for the rise in the level of water in the tank to be $7$ cm is

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. $2$

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

  3. $3$

  4. $2\dfrac{1}{2}$

Show answer
Correct Option: A
Explanation:

Water
flowed by the pipe in lh = $\pi r^2h$
= $\dfrac{22}{7} \times$ $\dfrac{7\times 7}{100\times100}$ $\times 5000 m^3 =77m^3$
Volume
of expected water in the tank = $\frac{50 \times 44 \times 7}{100} = 154
m^3$ 
Required
time= $154/77 = 2 hrs$.

A circle is inscribed in a quadrilateral ABCD in which $\angle B = 90^o$. If $AD = 23 cm$, $AB = 29 cm$ and $DS = 5 cm$. Find the radius of the circle.

maths geometric constructions circumscribing and inscribing a circle on a regular hexagon construction of tangent to a circle construction of tangents

  1. $11$ cm

  2. $13$ cm

  3. $9$ cm

  4. None of these

Show answer
Correct Option: A
Explanation:

$AS$ and $AP$ are tangents drawn to the circle at $A$

$\implies AS = AP$

Similarly

$BP = BQ$

$QC = CR$

$RD = DS$

Given

$AD = 23$

$\implies AS + SD = 23$

$AS = 23 – 5 = 18 = AP$

$AB = 29 \implies AP + BP = 29$

$\implies 18 + BP = 29 \implies BP = 11cm$

Now consider rectangle $PBQO$

$PB – BQ , OP = OQ = radius$

$\angle PBQ = 90$    

WKT

$OP \perp BP $ and $OQ \perp BQ$

Since radius is perpendicular to tangent at point of contact

$\implies$ All the angles are 90 degree and adjacent sides are equal

So, It is a square

$\implies r = BP = 11cm$

Given are the steps are construction of a pair of tangents to a circle of radius $4$cm from a point on the concentric circle of radius $6$cm. Find which of the following step is wrong?
(P) Take a point O on the plane paper and draw a circle of radius OA$=4$cm. Also, draw a concentric circle of radius OB$=6$cm.
(Q) Find the mid-point A of OB and draw a circle of radius BA$=$AO. Suppose this circle intersects the circle of radius $4$cm at P and Q.
(R) Join BP and BQ to get the desired tangents from a point B on the circle of radius $6$ cm.

maths geometric constructions circumscribing and inscribing a circle on a regular hexagon construction of tangent to a circle construction of tangents

  1. Only (P)

  2. Only (Q)

  3. Both (P) & (Q)

  4. Both (Q) & (R)

Show answer
Correct Option: B