Observing Hexagons in Intersecting Circles

Q.

A circle centered at O and of radius 3.5 cm is divided into six equal parts as shown in the figure below.

If the endpoints of these lines are joined, then the 2D shape so obtained is

1. an isosceles triangle

2. a star

3. a regular hexagon

4. an equilateral triangle

Q.

A circle centered at O and of radius 5 cm is divided into six equal parts as shown in the figure below.

If the endpoints of these lines are joined, then the 2D shape so obtained is

1. a regular hexagon

2. an isosceles triangle

3. a star

4. an equilateral triangle

Q.

In a quadrilateral MIST, MI = 3.5 cm, IS = 6.5 cm, $\angle M$ = ${75}^{\circ }$, $\angle I$ = ${105}^{\circ }$ and $\angle S$ = ${120}^{\circ }$. Which of the given line segments could be drawn first to construct the quadrilateral ?

1. ST

2. IS

3. IM

4. TM

Q.

Three circles each of radius 4 cm is constructed in such a way that the centre of each touches the circumference of other as shown in figure. The figure ABCDEF will be a

1. regular hexagon
2. regular pentagon
3. regular star
4. circle

Q.

Draw a circle and any two of its diameters. If you join the ends of these diameters, what is the figure obtained? What figure is obtained if the diameters are perpendicular to each other? How do you check your answer?

Q.

Three circles each of radius 5 cm is constructed in such a way that the centre of each touches the circumference of other as shown in figure. The length BC is equal to

1. 10 cm

2. 5 cm

3. 2.5 cm

4. 15 cm

Q. 3 circles each of radius 5cm is constructed in such a way that the centre of each touches the circumference of other as shown below. The length BC is.

1. 2.5 cm
2. 5 cm
3. 10 cm
4. 15 cm

Q. Which of the following is not true about a regular hexagon?

1. 6 equal angles
2. 6 equal sides
3. 6 sided polygon
4. Each angle is 60 degrees

Q.

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

1. 4 cm

2. 10 cm

3. 2 cm

4. 8 cm

Q. The polygon which has 6 equal sides is called a regular hexagon.

1. True
2. False