# Trzados polygons with compass

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**Mapping the equilateral triangle knowing his side:** 1. Draw a line segment *AB* with the value given side.

2. Doing center successively at the vertices *A* and B with a compass opening equal to *AB,* two arcs are drawn to determine the point C, the vertex opposite the side *AB.* 3. The triangle order is obtained by combining *C* with *A and B. Tracing knowing his side of the square 1. Side AB is drawn given. 2. Rose a perpendicular line on each of the vertices A and B with the squad and the bevel. From A draw a line forming oblique side AB with an angle of 45 °. This line determines the point C perpendicular to the cut in 6. 3. Simply drawing a parallel to AB through C, we obtain the square. Mapping the Pentagon knowing his side 1. Draw the side AB with the given value and is its bisector, so you get the point P. 2. Rose a line perpendicular to B, and from this point, and BA radio, it makes an arc that determines the point J to cut the perpendicular before. 3. With PJ and radio center P is drawn an arc cut at point M to the extension of AB. 4. Building Site A, and an opening of a bar AM, draw an arc that defines the point D on the bisector. 5. Finally, we draw arcs with center D, A and 6, and radius equal to the side AB. These arcs, when cut together, determine the points C and E, vertices of the pentagon. The pentagon is obtained by joining the points C, D and E with ends A and B. Tracing the regular hexagon knowing his side the regular hexagon is the only regular polygons which equal meets him and the radius of the circumcircle him. This easier to build, because if we give the value side or circumscribed radius, we can always build the same way. 1. Draw a circle of radius r equal to the side and a diameter AB as anyone, AD. 2. With center A and radius AO describes an arc cutting the circumference at points 8 and F. Similarly, with center D OJ is traced with radio *

an arc re-cut to the circumference at points E and C. 3. By joining these points together we obtain the hexagon. Razado the regular heptagon T knowing his side 1. Draw the side AB and draw a perpendicular

one end, for example 8. It also traces the bisector of this side. 2. In the end A, on AB, we construct a 30 ° angle, extending the side until they cut the perpendicular from 8 in the point P. To do this angle has carried the 30 degrees offered by the bevel. 3. With center A and radius AP describes an arc to cut the bisector of AB. missing information. Tangencies: It is said that two FIGRA are tangent if they have one thing in common, which is known as point of contact. The harmonious union between curves and straight lines or curves with each link is called and the union must take place by contact.. 18

The tangencies between circles can occur between circles and straight lines between polygons and lines between circles and polygons, and so on. However, the most common tangencies in the geometric designs are those that are generated between lines and circles, circles and among each other.

**I Basic properties of tangencies**

Tofix the exact paths tangencies, be taken into account the following theorems:

To

**- First Theorem:**A line is tangent to a circle when they each only one point

*(M)*

common, and the line is perpendicular to the radius of the circle at the point

**- Second Theorem:**a circle is tangent to two lines intersect if your institution is located in the bisecting angle between the

straight.

**- Third theorem:**two circles are tangent if they have a common point

*(N)*aligned with the centers of the circles.

**Trazadode a tangent line to a circle known as a point P on the same line**

1. Radius is drawn joining the OyP.2. The following is drawn through the point

*P*the line perpendicular to the radius that is tangent r sought.

**- Soul circumference Trazadode known tangents from a point**

P external to s1. He joins point

P external to s

*P*with the center of the circle, O, and perpendicular bisector of segment

*OP*thereby obtaining the point

*H.*2. With radio

*HO*Hy

*center,*draw an arc cutting the given circle in the points

*M*and M ', which are points of contact. 3. The tangent lines

*r*and s are to join the point

*P*with M and M '.

**- Drawing a circle of known radius tangent to two lines converging rys (Fig. 4.24)**

1. The perpendicular bisector of the angle determining the straights. 2. T draw a straight line parallel to one of the given lines and separated from it, the measure of radius

*r*known. The intersection of

*t*with the bisector is the center of the circle to be drawn. 3. The tangent points are M and

*M ',*which are drawing the radii perpendicular to the lines r and s.

**Drawing a circle through the point Al and**1. Since

*P*is tangent to the line*r**M and P*have to be points on the circle that you want to map, its center must lie in the bisector of

*MP. 2.*When P is the point of tangency at the line r, the center

*O of*the circle is located where the perpendicular from Par

*MP*crosses the

*bisector.*

**1. Or connect the dots and O'y is the midpoint of**

knowledge of different radio

*- Setting*external tangents to two circlesknowledge of different radio

*00 ',*which we call

*H. 2.*Draw a concentric circle to the largest radius that equals the difference between major and minor radii. 3. Centered at H and

*HO radio,*it makes an arc to cut the auxiliary circle at M and M '. 4. Or joins M and M ', thus resulting

*U and V: 5 points.*O'dos radios

*are*drawn parallel to 01 / and

*OU*to get the points S and

*T.*By joining I / with 7 and

*U-S,*the tangent lines are drawn ry /.

**- Setting internal tangents to two circles**

known and different radio1. Connect the dots O'y O and determines the midpoint of 00 ', which is

known and different radio

*H. 2.*Draw a circle of radius

*r*over

*r 'and*with the center O. 3. It is another circle with radiusHO and center

*H,*which intersects the former at the points

*M*and M '4. Joining the points

*M and M 'with*O, thus obtained aue

*M.*

**Tracing a circle of radius r tangent to another circle known outside with center at P (Fig. 4.28)**1. It extends a radius of O containing the point P. 2. It adds the radius r from P and obtained O '. 3. Finally, draw a circle with center is looking at radio O'y O'P.**-**Drawing a circle tangent to other known at a point M and passing through another interior point N (Fig. 4.29) 1. When M and N points on the same circumference, the center will be on the bisector of / W / V. 2. It binds with M and O, which cuts the bisector, we obtain the circumference O'Dea center, which will draw radio O'N.**-**Drawing a circle of known radius r, tangent to another circle and a given line 1. Draw an arc with center at O and having as radius the sum of the radius of the circle given over the radio conocido.2. Draw a line parallel to the view that it gave the radio measurement is known. The intersection of this arc is parallel with the center O of the circumference sought, and the points M and N are the points of contact.