In Fig. 3, a triangle $ABC$ is drawn to circumscribe a circle of radius 4 cm such that the segments $BD$ and $DC$ into which $BC$ is divided by the point of contact $D$ are of lengths 6 cm and 8 cm re

Question

In Fig. 3, a triangle $ABC$ is drawn to circumscribe a circle of radius 4 cm such that the segments $BD$ and $DC$ into which $BC$ is divided by the point of contact $D$ are of lengths 6 cm and 8 cm respectively. If the area of $	riangle ABC$ is $84$ cm$^2$, find the lengths of sides $AB$ and $AC$.

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Accepted Answer

Step 1: $BF = BD = 6$ cm
$CE = DC = 8$ cm
Let $AF = AE = x$ cm
Step 2: $\Rightarrow AB = (6 + x)$ cm, $AC = (8 + x)$ cm & $BC = 14$ cm
Step 3: Area of $	riangle ABC = \frac{1}{2} 	imes [p] 	imes r = \frac{1}{2} 	imes (28 + 2x) 	imes 4 = 84$
$\Rightarrow 14 + x = 21 \Rightarrow x = 7$ cm
Step 4: $\Rightarrow AB = 13$ cm, $AC = 15$ cm

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