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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