# PRINCIPLES OF TANGENCY 2

PRINCIPLE OF TANGENCY ( CONT’D)

C. CONSTRUCTING A TANGENT BETWEEN TWO UNEQUAL CIRCLES

Procedure
(Given R=30 and r=20)

1. Draw the given circles with centres O1 and O2.
2. Join O1-O2 and bisect at x. ( O1-O2 = 80)
3. Centre at x, radius xO1, draw a semicircle.
4. Centre at O1, radius R-r ( i.e. 30 – 20 = 10), draw a circle.
5. Draw a line O1z from O1 passing through y.
6. Draw line O2p parallel to O1z.
7. Join pz to get the required tangent.

D. CONSTRUCTING TRANSVERSE/INTERIOR/ CROSS TANGENTS TO TWO CIRCLES OF EQUAL RADII
Procedure
(Given R= 30)

1. Draw the two given circles with centres O1 and O2. (O1- O2 = 80).
2. Join O1 and O2 and bisect it at p.
3. Bisect pO1 and pO2 at q and R respectively.
4. Centres at q and R and radius QP and Rp respectively, draw two circles which are tangential to each other at p.
5. Join ST and UV to get the required tangents.

E. CONSTRUCTING TRANSVERSE TANGENT TO CIRCLES OF UNEQUAL RADII
Procedure
(Given R= 20, r= 15)

1. Draw the given circles with centres at O1 and O2. (O1-O2 =80).
2. Join O1 and O2 and bisect it at p.
3. Centre at O1, radius R+r, draw a circle.
4. Centre at p, radius pO1, draw a semicircle.
5. Join AO1 to intersect the given circle at C.
6. Centre at p, radius PC, cut the given small circle at q.
7. Join qC to get the required tangent.