Informational Encyclopedia

Fig a :

Given an acute angle, it is required to obtain a circle of any given radius tangential to both its arms.

Method: Suppose the circle is to be drawn on the given dimension. Obtain lines known as loci parallel to diagonal and base lines.(given distance on figure is 3/4"). These lines intersect each other and provide a point where u can draw a circle tangent to both arms.

Fig b:

Given a circle, it is required to obtain circles tangential to its circumference.

Method : Draw three circles at given dimensions. Draw parallel locus (loci drawn in previous method) lines. Draw parallel circles at there tangents points.

Fig c :

Tangency  to  parallel circles tangents.

Method : Draw three parallel lines as drawn on the fig c. (Both horizontal and vertical lines.) Here you will get the circles center points. These circle will intersect each other at there tangency.

Fig d :

Given two circle which are not tangential , it is required to obtain two other of given rad. tangential to them externally.

Method : Draw horizontal and vertical center lines. Draw two circles with given length radius. Draw two circles arc respectively. then you will get small circle center points.

Fig e :

Obtain a circle which shall be tangential to the larger circle internally and to the smaller circle externally.

Fig f: 

Obtain circles tangential to the mid point of the straight vertical line.

Method : Draw a line perpendicular to the horizontal line. This horizontal line consist of the centers of the given radius circles.

Fig g :

Draw an ogee curve between two parallel straight lines.

Fig h-i-j

Draw fillets or rounds when the angles are acute(fig j) , right (fig h) and obtuse (fig i)

Method: The center of any circle tangential to the arms of an angle lies on the bisector of the angle. Therefore we may bisect the angle.

Common tangency practice in engineering drawing/machine parts is shown in fig.

The sides of the figures are tangents to the circles.

(a) Circumscribe a square about a circle.

Draw a square and divide its all lengths, then you will get your center point. Draw a circle tangent to the sides.

(b) Circumscribe an equilateral triangle about a circle.

Draw a equilateral triangle with angles of 60 degrees by using set-square. Draw three lines from center of line to the end of the edges of triangle, you will get the center point. From the center point draw a circle tangent to the triangle.

(c) Circumscribe a hexagon about a circle.

Draw a hexagon with the angle of 120 degree. The draw lines from edges to edges. From center point draw a circle tangent to the sides.

(d) Circumscribe a octagon about a circle.

Draw a regular octagon with 135 degree angles. Then use same method as above mentioned.

The sides of the figures are chords of the circles are called inscribed figures.

(a) Inscribed square within a circle

Draw a square and then use same method as mentioned in the circumscribed method, but you will pick the chords to draw a circle.

(b) Inscribed triangle within a circle.

Draw same method drawing as above mentioned in the circumscribed figures, but pick the end point to draw a circle.

(c) and (d) Inscribed hexagon/octagon within a circle.

Drawing is same but use end point to draw a circle.

When two straing lines meet at a point they are said to form a angle.

The angle which is less than 90 degree is called acute angle.

The angle which is greater than 90 degree but less than 180 degree.

The angle which is equal to 180 degree is called straight angle.

Reflex angles are greater than 180 degree but less than 360 degree.

The angles which lies on either side of a common arm. 

Are equal to 90 degree.

When two angles together make 90 degree, they are said to be complementary. 

When two angles together make 180 degree, they are said to be supplementary.

We usually measure angles in degrees. A degree is a unit of angular measure. We may define it as one-ninetieth of the angular space between two lines at right angles to each other. 

For the measurement we use the units,

                60 Seconds = 1 Minute

                60 Minutes = 1 Degree

                60 Degrees = 1 Right Angle.

Protactors are used to measure the angles from 0 to 180 degrees. They are usually either semicircular or rectangular in shape. 

Set squares are also used to measure the angles like 30,45,60 and 90 degrees. Set square can be used singly and together.