Question

a triangle ABC is drawn to circumscribe a circle of radius 4 cm such that the segment ab and BC into which BC is divided by point of contact D are of length 8cm and 6cm respectively .find the sides ab and ac .



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Answer 1

Answer:

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Step-by-step explanation:

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Answer 2

Answer:

Let there is a circle having center O touches the sides AB and AC of the triangle at point E and F respectively.

Let the length of the line segment AE is x.

Now in △ABC,

CF=CD=6 (tangents on the circle from point C)

BE=BD=6 (tangents on the circle from point B)

AE=AF=x (tangents on the circle from point A)

Now AB=AE+EB

⟹AB=x+8=c

BC=BD+DC

⟹BC=8+6=14=a

CA=CF+FA

⟹CA=6+x=b

Now

Semi-perimeter, s=2(AB+BC+CA)

s=2(x+8+14+6+x)

s=2(2x+28)

⟹s=x+14

Area of the △ABC=s(s−a)(s−b)(s−c)

=(14+x)((14+x)−14)((14+x)−(6+x))((14+x)−(8+x))

3x−x=14

2x=14

x=214

x=7

Hence 

AB=x+8

AB=7+8

AB=15

AC=6+x

AC=6+7

AC=13

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