You will need

- A sheet of paper, compass, ruler, pencil

Instruction

1

With a compass draw on paper a circle of the desired diameter with the center at point O. the Construction of a regular five-pointed star represents a task similar to the writing in the circle a regular Pentagon.

2

Swipe through the circumference of diameter AB, placing it horizontally.

3

Restore the perpendicular CD to the line AB at the point O. To do this, draw circles with centers at the points A and b with the same radius, and then draw a straight line through the points of intersection of these circles.

4

Similarly, divide the interval AO point E in half. For dividing the cut the swipe the circle of the same radius with centers at points A and C. Now connect the points of intersection of the circle line - it will divide the segment exactly in half AO.

5

Swipe from point E the circle of radius CE and find the point F of intersection with the segment AB. Segment CF is the desired segment equal to the side of the inscribed Pentagon.

6

From point C, located at the top of the circle, apply consistently around the entire circumference level so that they are arranged at a distance from each other equal to CF. The circumference will be divided into five equal parts. The exact division is possible only with careful building by using a good compass.

7

Join the circle of the five points in such a way to make a five-pointed star. For this you will need a ruler.

8

If necessary, auxiliary lines inside the circle to erase with an eraser, so they do not spoil the look of a star. You can also delete all the other strokes used in constructing the figure.

Note

In order to draw a regular star, it is necessary to break a circle into 5 equal parts, i.e., the corner turns of 72°. I struggled for a long time trying to make that happen and to find their own proportions and dependencies, but I failed. Not enough soobrazhalki.

Useful advice

How to draw a seven-pointed star. Swipe the circle and put her five points separating it into equal arcs. Connect the dots by line segments. Turned pentagons. If each point of the chords to connect the two adjacent, we get the correct 5-sided polygon inscribed in a circle.