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

Construction -

Step 1 : 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 succesion.

Step 4 : Mark an arcs as $AB$ and join them together with a dotted line as well as with the centre C to form a triangle $ABC$.

Explanation : 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 $60$ degrees and only $6$ such angles are sufficient to form a circle as we know a circle of $360$ degrees.To form $6$ such angles we need to draw $6$ equilateral triangle or we can say we need to cut $6$ arcs on the circle with each of length of the radius in seccesion.