 # 8.3 Common Tangents

8.3 Common Tangents
A common tangent to two circles is a straight line that touches each of the circles at only one point.

1. Intersect at two points
(a) Circles of the same size
 Number of common tangents Properties of common tangents Two common tangents: AB and CD AC = BD AB = CD AB parallel to // OR parallel to // CD

(b) Circles of different sizes

 Number of common tangents Properties of common tangents Two common tangents: ABE and CDE AB = CD BE = DE OA // RB OC // RD

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

3. Do not intersect
(a) Circles of the same size

 Number of common tangents Properties of common tangents Four common tangents: AB, CD, PS and RQ AB = CD = OV PS = RQ AB // OV // CD

(b) Circles of different sizes

 Number of common tangents Properties of common tangents Four common tangents: AB, CD, PS and RQ AB = CD BT = DT PS = RQ OA // VB OC // VD

### 1 thought on “8.3 Common Tangents”

1. Thank you so much for your notes! They are simple yet understandable