TO DRAW AN ARC TANGENT TO A LINE AND PASSING THROUGH A POINT

Q. Draw an arc of radius 24 mm passing through a point 18 mm away and tangential to a line 50 mm length.
Solution:
Procedure:
“P” is the point. AB is the line and R is the radius of the arc which has to be drawn passing through the point P and tangential to the line AB. Draw a line parallel to AB at a distance R (24 mm) from it. With Pas centre and radius R, draw an arc to intersect the line at O. Now O as centre and radius R, draw the required arc as in Fig.

TO DRAW AN ARC TANGENTIAL TO TWO GIVEN LINES

The two given lines to which an arc of given radius has to be tangential may be, at right angles, or at an acute or obtuse angle, however the constructions procedure is common to all the three cases.

Q. Draw an arc of radius 22 mm tangential to two lines, (i) at 90° to each other, (ii) at an acute angle of 63° and (iii) at an obtuse angle of 112°

SOLUTION:
For Drawing an ARC Tangential to Two Given Lines (Common Procedure) : AB and CD are the two lines and R is the radius. Draw lines parallel to AB and CD at distance R, to intersect each other at O. With O as centre and radius r, draw the required arc. (Fig.).

 

 TO DRAW AN ARC OF CIRCLE TANGENTIAL TO A CIRCLE AND PASSING THROUGH A POINT

Q. Drawn an arc of radius 20 mm tangential to a circle of radius 36 mm and passing through a point 20 mm away from the bigger circle.

SOLUTION:

Procedure:

“P” is the point and the circle is of radius R. An arc of a circle is of radius “r” should be drawn passing through the point “P” and tangential to the circle.

With “P” as centre and radius “r” as 20 mm draw an arc. With O₁ as centre and radius (R+ r) i.e., 56 mm, draw another arc to intersect the previously drawn arc at O2. With O2 as center and radius “r” draw the required arc which pass through P and also tangential to the circle of 36 mm radius.

TO DRAW AN ARC TANGENTIAL EXTERNALLY TO A CIRCLE AND A LINE

Q.Draw an arc of 14 mm radius tangential externally to a circle of 20 mm radius and to a line of any length

SOLUTION:

AB is the line and the circle is of radius R (20 mm). It is required to draw an arc of a circle of radius 14 mm tangential to the circle and to the line AB. With O{1} as centre and radius (R + r) draw an arc. Draw a line parallel to AB at a distance r to intersect previously drawn arc at O{2} With O{2} as centre and radius r, draw the required arc, which will be tangential to both the circle and the line. (Fig.).

 

 TO DRAW AN ARC TANGENTIAL INTERNALLY TO A CIRCLE AND A LINE

Q.Drawn an arc of radius 14 mm, tangential internally to a circle 20 mm radius and to a line.

SOLUTION:
Procedure:

AB is the line and the circle is of radius R. It required to draw an arc of a circle of radius tangential to the circle and to the line AB. With O{1} centre and radius (R – r) draw an arc. Draw a line parallel to AB at a distance r to intersect the previously drawn arc at O{2} With O{2} as centre and radius r, draw the required arc, which will be tangential to both the circle and the line. (Fig.).