Advice 1: How to construct a Pentagon with a compass

Correct a Pentagon is a polygon in which all five parties and all five angles are equal. Around it is easy to describe a circle. To build the Pentagon and will help this circle.
How to construct a Pentagon with a compass
Instruction
1
You first need to build the compass circle. The center of the circle may coincide with point O. draw the axis of symmetry perpendicular to each other. At the intersection of one of these axes with the circle put a point V. This point will be the pinnacle of the future Pentagon. At the intersection of the other axis with the circle place the point D.
2
On the segment OD, find the middle and mark it point A. then you need to build a compass a circle with center at that point. In addition, it must pass through the point V, that is, the radius of CV. The point of intersection of the axis of symmetry and the circle label for V.
3
Then, using the compass , swipe a circle of the same radius by placing a needle in the point V. the Intersection of this circle with the original label as a point F. This point will be the second top right of the future Pentagon.
4
Now we need to make the same circle through the point E, but with the center at the Intersection of F. only that the circle with the original label as a point G. This point will become a vertex of the Pentagon. Likewise, to build another round. Its center at G. the Point of intersection of its circumference with the original let it be H. This is the last vertex of a regular polygon.
5
You should have five vertices. Do they just connect on the line. As a result of all these operations you will get inscribed in a circle right Pentagon.
Useful advice
In this simple way, it is possible to construct a Pentagon. To build the triangle, you must spread the legs of the compasses at a distance equal to the radius of the circle. Then at any point install the needle. Fine auxiliary circle. Two points of intersection of the circles and the point at which was the compasses formed by the three vertices of the triangle.

Advice 2 : How to find the circumcenter

Sometimes around a convex polygon you can draw a circle so that the tops of all the angles lying on it. Such a circle relative to the polygon should be called described. Her center does not have to be inside the perimeter of the inscribed figure, but using the described properties of the circle, to find this point is usually not very difficult.
How to find the circumcenter
You will need
  • Ruler, pencil, protractor or straight edge, a compass.
Instruction
1
If the polygon about which it is necessary to describe a circle drawn on paper, for finding the centreof the circle and quite a ruler, pencil and protractor or angle. Measure the length of any of sides of a shape, determine its middle and put in this part of the drawing auxiliary point. With the help of the set square or the protractor guide on the inside of the polygon perpendicular to the side segment to the intersection with the opposite side.
2
Do the same thing with any side of the polygon. The intersection of the two constructed segments is the required point. This follows from basic properties are described of a circle - its center in a convex polygon with any number of sides, always lies at the intersection of middle perpendiculars drawn to these parties.
3
For the regular polygons defining the center ofa inscribed circle can be much easier. For example, if it is a square, then draw two diagonals and their intersection will be the centerom of the inscribed circle. The regular polygon with any even number of sides, it is sufficient to connect the auxiliary segments two pairs lying opposite each other at the corners - center of the described circle must coincide with the point of their intersection. In a right triangle to solve the problem just define the middle of the longest side of the figure is the hypotenuse.
4
If conditions are unknown, whether it is possible in principle to draw a circumscribed circle for that polygon, after determining the proposed point centerand any of the described ways you can find out. Mark on the compass the distance between the found point and any vertices, set the compass at the intended center of the circle and draw a circle, every vertex must lie on this circle. If not, then not running one of the basic properties and describe a circle about a given polygon is impossible.
Is the advice useful?
Search