Technical Drawing

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Tangencies

Make the tangent:

"Two circles:

1. External Tangents: Draw another concentric to the largest radius Rr, join the centers, is the bisector, and draw a circle assistant to the centers. He joins the center with the points of intersection with the smaller circumference, and extend, where the couple will cut the tangent points. They are made parallel to the minimum, finding all points of contact.

2. Internally tangent: It works the same, except that the circle is of radius R + r, and that are parallel to the opposite side.

-In another circle, which passes through P:

If going abroad is to be a concentric circle of radius R + r, and from a radius R P, which cut the other centers are the solutions.

If you will be internal, but like subtracting instead of adding radio.

"On both sides of an angle:

We make the bisector, and a separate parallel to the radio side, we get the center.

-In another circle in a point on this:

He joins the center with T, is prolonged and the extension is put on the radio.

"The bond of 2 circles:

1. Concave, Track 2 concentric circles adding to each the radio link, cut points are the centers.

2. Convex, but it operates like concentric with the radio link minus the circle.

-To another at one point, and passing through a point P:

Join the center with T and prolonged. Join T with P and we make the bisector, the cutoff point is the center.

The straight-link 2:

Become parallel separate the radius, the cutoff point is the center

-The connection of two lines with arcs of different radius:

From the ends of each line are placed perpendicular, and they put a greater distance than that between the respective ends. Joining these points and is its bisector. The first center will be the court where the perpendicular bisector in the outermost (considering the outermost which is situated further away from the opposite ends of the line), the second will be the end of the other perpendicular. The junction between arches we find by joining the centers and extend that line.

-A one line and passing through a point P:

Rose a perpendicular T-joins PT, is its bisector, and the cut is perpendicular to the center.

-Tangent to a line and passing through A and B:

Joining A and B, is its bisector, provides an auxiliary circle passing through A and B, it becomes a tangent from C (cut straight to the ER), travels the length of the tangent on both sides of C, are constructed across T1 and T2, with the bisector cuts are the centers.

-Circle tangent to the sides of an angle, passing through P:

It is the bisector and P moved below it, finding P ', join them, and continues. It is a circle centered on the bisector passing through P and P 'and operated as before.

-Tangent to a straight and a circle at a point on this:

We join with the middle T and prolonged. We make a line perpendicular to the tee, which will cut the line. The centers will be in the supplementary angles bisectors found, so they will be at the intersection of this with the line joining T and downtown.

-Tangent to another passing through A and B.

They join, is its bisector. It is a circle centered at her assistant and passing through A and B and is drying in the other. One is the ER of both, and from where you cut the prolongation of AB do given tangent to the circumference. Join the center with T1 and T2, expanding, and cuts the bisector d AB are the centers.

-Circle tangent to two others, at one point one of them (like operating with: passing through a point and be tangent to another):

1. T join the center, expanding. We raise a perpendicular to it by T. We make a circle passing through T and the other is drying. We found the ER, where ER court with each other, we tangents to the second round, and it operates just like before.

2. It adds or subtracts the radius of the second from T, it joins the center of the second and is the bisector, cuts with a straight line connecting the center with T are the centers

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