For a festive decoration, stars are often needed. They can have an irregular shape and a different number of rays, and then they can be cut out of paper without any construction. However, to decorate the top of the Christmas tree or the towers of the Moscow Kremlin, you need the correct five-pointed stars. You can build them using the most common drawing tools.
It is necessary
- - paper;
- - compasses;
- - ruler;
- - square;
- - pencil.
Instructions
Step 1
Draw a circle of any diameter. Note that the star will be inscribed in a circle, so the radius should roughly correspond to the desired length of the ray from the center to the top. For convenience, mark the center with point O. Draw the horizontal diameter through it. At point O, draw a perpendicular to it and extend it to the intersection with the circle. Designate the lower point as M.
Step 2
Divide the radius from point O to the left in half. Put point A. You can connect it with a dotted line to point M, but this is not necessary. Spread the legs of the compass at a distance of AM. Draw an arc of this radius from point M to the intersection with the second horizontal radius. Set point N. Describe another arc with radius AN. Put point K.
Step 3
Draw a circle with a radius of AK. Find the points of its intersection with the first circle. Label them as C and D. Thus, you already have 3 vertices of the star. It remains to find 2 more. To do this, draw circles of the same radius equal to CA from points C and D. Mark the points of their intersection with the base circle. Connect the vertices of the rays with dashed lines. You now have a regular pentagon. Extra lines can be removed, leaving only the contours of the pentagon and the center of the circle.
Step 4
Write a circle in the resulting pentagon. Since you are dealing with a regular convex polygon, the center of the inscribed circle coincides with the center of the circumscribed, that is, the original. Draw perpendiculars to the points where the sides of the pentagon touch the new circle. Set aside equal distances from the points of their intersection with the sides or from the center. Connect the resulting points to the vertices of the pentagon. Trace the outline of the star and delete unnecessary constructions.
