Observation of Triangles in Intersecting Circles

Q.

A circle centered at O and of radius 3 cm is divided into six equal parts as shown in the figure below.

If A is joined to C, C is joined to E and E is joined to A, then the 2D shape so obtained is ________.

1. an equilateral triangle

2. a regular hexagon

3. an isosceles triangle

4. a star

Q. State True or False:
A line can be taken as a circle with infinite radius and a circle can be assumed to be a polygon with infinite sides.

1. True
2. False

Q.

A circle centered at O and of radius 4 cm is divided into six equal parts as shown in the figure below.

If we join alternate points starting from A, then the 2D shape so obtained is

1. an isosceles triangle

2. a star

3. an equilateral triangle

4. a regular hexagon

Q. 2 circles of radius 3 cm each is constructed such that centre of each touches the circumference of other as shown below.
$A{C}_1{C}_2\text{is a/an}$.

1. isosceles triangle
2. equilateral triangle
3. scalene triangle

Q.

Two circles of radius 3 cm each is constructed such that centre of each touches the circumference of other as shown in figure. The triangle $A{C}_1{C}_2$ is

1. Scalene
2. Isosceles
3. Right - angled
4. Equilateral

Q. ABC is an equilateral triangle inside a circle with centre O. What is the measure of angle AOC?

1. 60 degree
2. 120 degree
3. 150 degree
4. 180 degree

Q. In triangle PQR, PQ = 5 cm and PR = 6 cm, which of the following can't be the third side?

1. 9 cm
2. 3 cm
3. 4 cm
4. 21 cm

Q. Explain how to construct an equilateral $△ABC$ of side $5cm$, with the help of compass and ruler.