You will need
- - the range;
- a pair of compasses.
Theorem the circumcenter is the center of the intersection of middle perpendiculars. The figure shows that each side of the triangle, the perpendicular drawn from its middle and the segments connecting the point of intersection with the vertices form two equal right-angled triangle. The segments MA, MB, MC are equal.
You are given a triangle. Find the middle of each side – take a ruler and measure it. The resulting dimensions divide in half. Move from the vertices on each side, half the size. Check the results points.
From each point put perpendicular to the side. The point of intersection of these perpendiculars is the circumcenter. To find circle center with only two perpendicular lines. The third is built for self-examination.
Please note – triangle where all angles are acute, the point of intersection is inside the triangle. In a right triangle lies on the hypotenuse. In obtuse is beyond. And perpendicular to the side opposite the obtuse angle is not built to the center of the triangleand outside.
Measure the distance from point of intersection to any vertex of the triangle. Set this value on the compass. By placing the needle into the point of intersection, draw a circle. If it touches all three vertices of the triangle, you did the right thing.
There is a theorem of sines establishes a relationship between the sides of the triangle, its angles and radii of the circumscribed circle. This dependence is expressed by the formula: a/sina = b/sinb = C/sinc = 2R, where a, b, c be the sidelengths of triangle; sina, sinb, sinc sines of the angles opposite to these sides; R is the radius of the circle which is described around the triangle.