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  • In Fig. 4, a circle is inscribed in a ABC having sides BC = 8 cm, AB = 10cm and AC = 12 cm. Find the lengths BL, CM and AN.

In Fig. 4, a circle is inscribed in a \DeltaABC having sides BC = 8 cm, AB = 10cm and AC = 12 cm. Find the lengths BL, CM and AN.

 

 
 
 
 
 

Answers (1)

Given,

    AB = 10cm

    BC = 8cm

    AC = 12cm

    BL, CM, AN = ?

We know that tangents drawn from an external point to a circle are equal.

So,

    Let    AM = AN = x

              BN = BL = y

              CM = CL = z

    \\\Rightarrow x + y = 10 cm \\\Rightarrow y + z = 8 cm \\\Rightarrow z + x = 12 cm

\Rightarrow2( x + y + z ) = 30 \Rightarrow x + y + z = 15

Now, x + y = 10 cm \text{ and } x + y + z = 15

            \Rightarrow 10 + z = 15 \Rightarrow z = 5

            y + z = 8 \text{ and } x + y + z =15

            \Rightarrow x + 8 = 15 \Rightarrow x = 7

            x + z = 12 \text{ and } x + y + z =15

            \Rightarrow y + 12 = 15 \Rightarrow y = 3

AN = x = 7cm,    BL = y =3cm,    CM = 5cm

Posted by

Safeer PP

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