AB and CD are two common tangents to circles which touch each other at C.
Question:

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, then AB is equal to

(a) 4 cm

(b) 6 cm

(c) 8 cm

(d) 12 cm

Solution:

Let us first put the given data in the form of a diagram.

We know that tangents drawn from an external point will be equal.

Therefore,

AD = CD

Since CD is given as 4 cm,

AD = 4 cm

Similarly,

BD = CD

Therefore,

BD = 4 cm

AB = AD + BD

AB = 4 + 4

AB = 8 cm

Therefore, the answer to this question is option (c)

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