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

  1. 12 cm

  2. 11 cm

  3. 10 cm

  4. 9 cm

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 (a) 12 cm (b) 11 cm (c) 10 cm (d) 9 cm. Circles, ML Aggarwal Understanding Mathematics Solutions ICSE Class 10.

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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