How to find the circumcenter

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.

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.

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.

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.