Construction of Circumcircle in Regular Hexagon

Q.

Draw a regular hexagon of side 5 cm.

Q.

Construct a regular hexagon of side 4 cm. Construct a circle circumscribing the hexagon.

Q.

Draw an inscribing circle of a regular hexagon of side 5.8 cm and find the length of the radius.

1. 8.4 cm

2. 4.61 cm

3. 6.0 cm

4. 2.61 cm

Q. Construct a circle in a regular hexagon of side 3 cm. [3 MARKS]

Q. Question 194
Draw a circle of radius 3 cm and draw its diameter and label it as AC. Construct its perpendicular bisector and let it intersect the circle at B and D. What type of quadrilateral is ABCD? Justify your answer.

Q.

Draw a circle circumscribing a regular hexagon with side 5 cm.

Q. Construct a regular hexagon in a circle of radius 3 cm.

Q.

If the side of a regular hexagon is 8 cm, then its circumradius is equal to ____

1. To determine the centre of the circle.

2. Construct the radius of the bigger circle.

3. Determine the tangents to circle ‘D’ from a point on circle ‘C’

4. Construct the circle D

Q.

Construct a cyclic quadrilateral PQRS with PQ = 4 cm, QR = 6 cm, PR = 7.5 cm, QS = 7 cm

Q.

In fig., a circle with centre O is inscribed in a quadrilateral ABCD such that, it touches the sides BC, AB, AD and CD at points P, Q, R and S respectively, If AB = 29 cm, AD = 23 cm, ∠B = 90^o and DS = 5 cm, then the radius of the circle (in cm) is:

1. 6

2. 18

3. 11

4. 15

Q.

Construct a cyclic quadrilateral ABCD in which AB = 8cm, AC = 9 cm, BC = 7 cm, and AD = 5.4 cm.

Q.

Construct a regular hexagon of side 4 cm. Construct a circle circumscribing the hexagon and measure its circumradius.

1. 4 cm

2. 2 cm

3. 8 cm

4. 10 cm

Q. Construct a regular hexagon of side 4 cm. Construct a circle circumscribing the hexagon and measure its circumradius.
$\left[3Marks\right]$

Q.

Construct a cyclic quadrilateral EFGH with EF = 6 cm, $\angle GEF={60}^{\circ }$, FG = 7cm and $\angle EGH={50}^{\circ }$.

Q. If a circle is inscribed in an regular hexagon, which of the following must be true?

1. The hexagon circumscribes the circle.
2. The circle is tangent to each side of the hexagon.
3. Each vertex of the hexagon lies outside the circle.
4. The circle is congruent to the hexagon.

Q. Construct a regular hexagon in a circle of radius 3 cm.

Q. While constructing a circle circumscribing and inscribing a regular hexagon, identify the statement true for the construction?

1. circle outside and inside hexagon
2. only hexagon is constructed
3. only circle is drawn
4. outside hexagon and inside circle

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

1. $1m$
2. $3m$
3. $4m$
4. $2m$

Q. Construct a regular hexagon inscribed inside the circle with radius $3.2$ cm.

Q. 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

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 $(8,-5)$

Q.

Draw 2 concentric circles of radii 3cm and 5cm. Draw tangents to the inner circle from any point on the outer circle. Measure the length of the tangent. [4 MARKS]

Q. How many equal parts you will cut the circle to draw inscribing hexagon?

1. $4$
2. $6$
3. $7$
4. $5$

Q. Which tool will you use for cutting a circle into 6 equal parts?

1. ruler
2. divider
3. protector
4. compass

Q. Draw a circumscribing circle and inscribing hexagon whose radius is $2.5$ cm.

Q. Identify the construction used in the figure.

1. circle circumscribing and inscribing a regular hexagon
2. circle circumscribing and inscribing a circle
3. hexagon circumscribing and inscribing a regular hexagon
4. circle inscribing and circumscribing a regular hexagon

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

1. $\frac{2\pi r}{6}$
2. r
3. $\frac{\pi r}{6}$
4. $\frac{r}{2}$

Q. Sketch circles circumscribing and inscribing a regular hexagon whose radius is $2$ m.