Question

Draw a circle, Identify a point on it. Cut arcs on the circle with the length of the radius in succession. How many parts can the circle be divided into? Give reason.

Answer 1

Hint: To solve this type of problem first we have to write the steps of construction and from those steps we have to follow them one by one. To solve this we have to know the basic definitions of arc, radius of a circle.

Complete step-by-step answer:
Step 1: We have to draw a circle of radius R.
Step 2: Take a point A on the circle.
Step 3: Cut arcs on the circle with the length of the radius in succession.
Step 4: Mark an arc as AB and join them together with the centre C to form a triangle ABC.

Now as we can see the sides of the triangle i.e. AB, BC and CA are of equal length that is R. Therefore, the triangle ABC is an equilateral triangle.
 Now we know that all angles of an equilateral triangle are of \[{{60}^{\circ }}\] and only 6 such angles are sufficient to form a circle as we know a circle of \[{{360}^{\circ }}\].
To form 6 such angles we need to draw 6 equilateral triangles or we can say we need to cut 6 arcs on the circle with each of length of the radius in succession.

Note: After drawing an arc we have to take a radius distance from this arc to the next point on the circle and draw another. Similarly we have to draw successively. An equilateral triangle has three equal sides and three equal angles.