Jamuna has a circular piece of paper. She is trying to locate its centre. Amina gives her a suggestion. She follows the instructions and is thrilled to find that it works. Can you guess what Amina told her?
Amina likely told Jamuna to fold the circular piece of paper in half, and then fold it in half again. Because all points on the circle are at equal distance from the centre, folding the paper so that the curved edges align perfectly creates a crease that represents a line of symmetry passing through the centre.
By folding it a second time, another such crease is formed. The intersection point of these two creases will be the exact centre of the circle. This method works because of the inherent symmetries of a circle, ensuring that any line of symmetry must pass through its centre.
Explanation
The textbook context highlights that 'all points on the circle are at equal distance from the centre' and mentions the 'symmetries of a circle'. For a physical circular paper, folding it so the edges match exploits this equidistant property, creating a diameter. Two such folds intersect at the unique point equidistant from all edges: the centre.
Solution Steps
Step 1: Fold the circular piece of paper exactly in half so the edges meet, creating a crease.
Step 2: Fold the paper in half again to create a second crease.
Step 3: The point where the two creases intersect is the centre of the circle.