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PROBLEMS IN GEOMETRICAL DRAWING. 189
the arc b d through the center of the circle. The points of
intersection at b and d are the points where the required tan-
gents a b and a d will touch the circle.
To draw a tangent to a given point in
a given circle. (See Fig. 21).
Given circle and the point /z, x y is
required.
Solution
:
The radius is drawn to the point h and
a line constructed perpendicular to it at the
point k. This perpendicular, touching the
circle at h, is called a tangent.
Fig. 22.
To draw a circle of a certain size that
will touch the perphery of two given cir-
cles. (See Fig. 22).
Given the diameter of circles a, b,
and c. Locate the center for circle c,
when centers for a and b are given.
Solution
:
From center of a, describe an arc
with a radius equal to the sum of radii of a and c. From b as
center, describe another arc using a radius equal to the sum of
the radii of b and c. The point of intersection of those two
arcs is the center of the circle c.
Note.—This construction is useful when locating the center
for an intermediate gear. For instance, if a and b are the pitch
circles of two gears, c would be the pitch circle located in correct
position to connect a and b.
To draw an ellipse, the longest
and shortest diameter being given.
The diameters a b and c d are
given. The required ellipse is
constructed thus : (See Fig. 23).
From c as center with a radius
a u, describe an arc f1
f. The
points where this arc intersects a
b are foci. The distance fn is
divided into any number of parts,
as 1, 2, 3, 4, 5. With radius 1 to b,
and the focus/ as center, describe arcs 6 and 61
radius and with f1
as center describe arcs 6’
radius 1 to a and/1
as center, describe arcs intersecting at 6 and
C1
; with the same radius and with / as center, describe arcs
intersecting at 62
and.63
. Continue this operation for points 2,
3, etc., and when all the points for the circumference are in this
with the same
and 63
. With
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