(i) Tangential externally to the two given circles, or
(ii) Tangential internally to the two given circles, or
(iii) Tangential internally to one and externally to the other.
TANGENT EXTERNALLY TO BOTH THE CIRCLES
Q.Draw an arc of 32 mm radius tangential externally to two circles 32 mm and 18 mm radii.
SOLUTION
Procedure:
Two circles of radii R_{1} (32 mm) and R_{2} (18 mm) are given. It is required to draw an arc of radius r = 32 mm tangential to both the circles.
With O{1} as centre and radius (R{1} + r) draw an arc and with O{2} centre and radius (R{2} + r) , intersect former arc at C. Now with C as centre and radius r = 32 draw the required arc, which will be tangential externally to both the circles.
TANGENT INTERNALLY TO BOTH THE CIRCLES
Q.Draw an arc of 64 mm radius tangential internally to two circles of radii 32 mm and 18 mm
SOLUTION:
Procedure:
Two circle of radii R{1} (32 mm) and R{2} (18 mm) are given. It is required to draw an arc of radius r (64 mm) tangential internally to both the circles.With O{1} as centre and radius (r – R{1}) , draw an arc and O{2} as centre and radius (r – R{2}) draw an arc to intersect the former arc at C. With C as centre and radius r, draw the required arc, which will be tangential intemally to both the circles.
TANGENT INTERNALLY TO ONE CIRCLE AND EXTERNALLY TO THE OTHER
Q. Draw an are of 60 mm radius, tangent internally to circle 20 mm radius and externally to another circle of radiua 12 mm.
SOLUTION:
Procedure:
Two circles of radil R{1} (20 mm) and R2 (12 mm) are given. It is required to draw an arc of radius r (greater than one of the radii, say R{1} ) tangent internally to one and external to the other With O{1} the centre of internal tangent circle as centre, draw an arc with radius (r – R{1}) . With O{2} centre of external tangent circle as centre, draw an arc with radius (r + R{2}) to intersect the former arc at C. With C as centre and radius ras 60 draw the required curve which will be a tangent internally to one and externally to the other
TO DRAW A TANGENT TO A CIRCLE FROM A POINT OUTSIDE IT
Q.Draw a tangent to a circle of 20 mm, radius, from a point 60 mm outside the circle.
SOLUTION:
Procedure:
“P” is the point outside the circle, C is the centre of the circle to which the tangent is to be drawn from P the outside point. Connect CP and bisect it at O. With O as centre, CP as diametre, draw a semicircle to cut the given circle at Q. Connect PQ, the required tangent.
COMMON TANGENT TO TWO CIRCLE
Q.Draw a common external tangents to two given circles of equal radii (say 20 mm) the centres of which are 70 mm.
SOLUTION:
Procedure:
Draw the two given circles of equal radii (20 mm) at the given central distance. O{1} and O{2} are the centres of the two circles of equal radil. Connect O{1} O{2} and draw perpendiculars O{1} P and O{2} Q. Connect P and Q the required common external tangent
INTERNAL TANGENT
Q.Draw a common internal tangent to two given circles of equal radii [20 mm] of central distance 70 mm.
SOLUTION:
Procedure:
Draw the two circles at the central distance of 70 mm
O{1} and O{2} are the centres of circles of equal radii. Connect O{1}*O{2} and bisect it at A. Bisect O{1} A at C{1} and C2 between O{2}*A With C{1} and C{2} as centres draw two semi-circles to intersect the given circles at P and Q. Connect required common internal tangent P – Q
TWO CIRCLES OF UNEQUAL RADII
1. External Tangent:
Q.Draw a common external tangent to two circles of unequal radii say 26 mm and 20 mm, the central distance of which are 75 mm.
Solution:
Procedure:
O{1} and O{2} are the centre circles of unequal radii. R{1} & R{2} be radii of the two circles. With the radius (R{1} – R{2}) draw a circle. O{1} O{2}*i diametre draw a semi circle which intersect the circle of radius (R{1} – R{2}) at A. Produce it to meet R_{1} circle at P. Draw a line from 02 parallel to O{1}*A to cut circle at Q Le., Q*O{2} connect PQ the required external tangent.
2. Internal Tangent:
Q.Draw a common internal tangent to two circles of unequal radii of 26 mm and 20 mm, the central distance of which are 75 mm.
Solution:
Procedure:
O{1} and O{2} are the centres of two circles of unequal radii. With O_{1} as centre and radius (R{1} + R{2}) draw an arc of circle. With O{1} – O{2} as diameter, draw a semi-circle to cut the arc of circle of radius (R{1} + R{2}) at O. And draw O{2}*Q parallel to it that cuts the R{1} circle at P.
