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.
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A circle can be divided into 6 parts. The reason is that the sum of all the angles around a point is always 360°.
Steps of construction:
Draw a circle of radius r with center O.
Take a point on the circle and mark it as A.
From the point, A with the scale same as of the radius draw an arc and mark it as B.
Repeat the above step till we reach point A.
Total of 6 parts are obtained.
Join A, B and C, we obtain an equilateral triangle with the same sides and equal lengths 60°.
Like an equilateral triangle ABC, we obtain another such 5 triangles, a total of 6 equilateral triangles.
Therefore, in total the angle = 6 × 60° = 360°
Reason:
The sum of all the angles around a point is always 360°.
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