Mathematics
In the adjoining figure, sides BC, CA and AB of △ABC touch a circle at point D, E and F respectively. If BD = 4 cm, DC = 3 cm and CA = 8 cm, then the length of side AB is
12 cm
11 cm
10 cm
9 cm
Circles
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Answer
We know that if two tangents are drawn from an external point to a circle then, the lengths of the tangents are equal.
∴ BF = BD = 4 cm, CE = CD = 3 cm and AF = AE.
Given, CA = 8 cm.
From figure,
⇒ CA = AE + CE
⇒ 8 = AE + 3
⇒ AE = 8 - 3 = 5 cm.
We know AF = AE = 5cm.
From figure,
AB = AF + BF = 5 + 4 = 9 cm.
Hence, Option 4 is the correct option.
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