Tag: construction of tangent to a circle

Questions Related to construction of tangent 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) $

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

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

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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)

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Correct Option: B

What are the tools required for constructing a tangent to a circle?

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

  1. ruler

  2. compass

  3. pencil

  4. all the above

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Correct Option: D
Explanation:

The tools required for constructing a tangent to a circle is ruler, compass and pencil.

Let C be the circle with centre at $(1, 1)$ and radius $=1$. If T is the circle centred at $(0, y)$, passing through origin and touching the circle C externally, then the radius of T is equal to?

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

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

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

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

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

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Correct Option: A