2. Intersect at one point
(a) Circles of the same size
Number of common tangents |
Properties of common tangents |
Three common tangents:
AB, CD and PQ |
AC = PQ = BD
AB = OR = CD
AB // OR // CD
AC // PQ // BD
PQ perpendicular to OR |
(b) Circles of different sizes
(i) External contact
Number of common tangents |
Properties of common tangents |
Three common tangents:
ABE, CDE and PQ |
AB = CD
BE = DE
OA // RB
OC // RD
PQ perpendicular to ORE |
(ii) Internal contact
Number of common tangents |
Properties of common tangents |
One common tangent: PQR |
ONQ perpendicular to PR |