# How to draw a triangle in a circle

one single circle can be circumscribed about each triangle. Accordingly, the triangle is inscribed, that is so, all of whose vertices lie on the circle. Draw a triangle can be a piece of paper with a ruler, a protractor and a compass, as well as in AutoCAD.

### You will need:

- paper; - Drawing instruments; - The parameters of the triangle; - PC with AutoCAD software.

## Instruction how to draw a triangle in a circle

Step 1:

Calculate the radius of the circle in which you need to enter the triangle. In order to draw the triangle itself, you need to know the size of its three sides, two sides and a limited angle of two angles and the side between them. All dimensions are needed to calculate the radius. To build enough to know the length of the sides and the angle or the sizes of the two sides.

Step 2:

Depending on what you know, calculate the radius. It is the length of side divided by the sine of twice the angle of the opposite, that is R = a / 2sinα. You can find it, and by dividing the product of all the parties to quadruple the area, that is, R = abc / 4S. The denominator of the fraction, in turn, can be expressed as the square root of the expression p (p-2a) (p-2b) (p-2c).

Step 3:

Draw a circle. Designate it as a center point A. The same will be the orthocenter of the triangle, that is, the point of intersection of its midperpendiculars.

Step 4:

Spend radius and at the point of intersection of the set point A. This is one of the vertices of the triangle. In any case, the condition given the length of one of the parties. Draw this side to the other end of the segment was on the circle. It is most convenient to do with the pair of dividers. Dissolve the needle to a predetermined length and mark the point on the circle. Connect it to the vertex A. Replace point B.

Step 5:

To draw a second side, just dilute the legs of a compass on the second side length, mark the point C, connect it to the vertices B and A. Check the length of the SA side. If you fulfill all the right, then its length is equal to the specified size.

Step 6:

Knowing at least one angle, the construction will still start from the side. From one of the endpoints aside predetermined angle. Swipe through this new segment to the point of intersection with the circle. Check its length. It should be equal to the length of the second side. Put the point C Connect the points A and C line.

Step 7:

In AutoCAD program equilateral triangle can be drawn with the "Polygon" tool, putting in the window that appears, the desired number of parties. The program will prompt you to choose between the inscribed and circumscribed polygons. Select the first. The center of the circle is defined by coordinates or click on the screen.

Step 8:

Wrong triangle can be built in two ways in the program. It can consist of separate lines or polyline to be one that has the same start and end. Preferably, the first method. Building a little different from what you were doing on paper. Draw a circle of a specified radius. Designate a point on it. From this point of build with the tool "Line" segment to the intersection with the circle next cut position relative to the first predetermined angle. A third segment connects a point of intersection with the circumference of the two existing lines. The desired command can be called via the tab "Home" in the top menu or enter in the command prompt _line.