Answer is C. 8 cm
Given:
AB and CD are two common tangents to circles which touch each other at C. If D lies on AB such that CD = 4 cm
To find: length of AB
Solution:
Property: If two tangents are drawn to a circle from one external point, then their tangent segments (lines joining the external point and the points of tangency on circle)
Since c is the external point to the circles and two common tangents touch each other at c.
By the above property,
AD = BD = CD = 4 cm (tangent from D)
Now clearly,
AB = AD + BD
⇒ AB = AD + BD
⇒ AB = 4 cm + 4 cm
⇒ AB = 8 cm
Hence, AB = 8 cm
