Case Study: There is a circular park in a colony. The diameter of the park is 40 m. Three poles A, B and C have been eracted at equal distances on the boundary of the park. These poles have been connected with each other using straight wires, as shown in the figure.

Based on this information, answer the following questions:

1. The circumference of the circular park is :
(a) 125.6 m
(b) 130 m
(c) 251.2 m
(d) 257.2 m

2. A child cycles along the boundary of the park in clockwise direction. The distance covered by the child in going from B to C is :
(a) 41.8 m
(b) 83.7 m
(c) 20.9 m
(d) 125.6 m

3. ABC is :
(a) a scalene triangle
(b) a right triangle
(c) an equilateral triangle
(d) an isosceles triangle

4. If we draw perpendicular from B on AC, then it will pass through : (a) centre of the circle
(b) circumcentre of the circle
(c) centroid of the circle
(d) all the above

5. The length of the piece of wire used to connect any two poles is :
(a) 20 m
(b) 20$\sqrt{3}$ m
(c) 20$\sqrt{2}$ m
(d) 60$\sqrt{3}$ m

Assertion (A): In the figure, AB and AC are equal chords of a circle with centre O. If OD = 4 cm, then OE is also 4 cm.

Reason (R): Equal chords of a circle are equidistant from the centre.

1. A is true, R is false

2. A is false, R is true

3. Both A and R are true

4. Both A and R are false

Assertion (A): Equal chords of a circle subtend equal angles at the centre of the circle.

Reason (R): One and only one circle can be drawn passing through three points.

1. A is true, R is false

2. A is false, R is true

3. Both A and R are true

4. Both A and R are false

Two chords of a circle of lengths 10 cm and 8 cm are at the distances of 6 cm and 5 cm respectively from the centre. This statement is :

1. True

2. False

3. Can't say anything

4. Data inadequate