Question

The radius of the incircle of a triangle is 8cm and the segments into which one side is divided by the point of contact are 12cm and 16cm. Determine the other two sides of the triangle.... Please need answer with diagram explanation ..

Answer 1

Answer:

Correct option is A)

BF=BD=6cm

[length of tangent from external point are equal]

CE=CD=8cm

[length of tangent from external point are equal]

Let AF=AE=x

[length of tangent from external point are equal ]

Now,

AreaofΔABC=AreaofΔAOB+AreaofΔBOC+AreaofΔCOA

=

2

1

×4(6+x)+

2

1

×4(14)+

2

1

×4(8+x)

=

2

1

×4(28+2x)

=4(14+x)

Also, area of ΔABC by Heron's formula

S=

2

14+6+x+8+x

=14+x

Area of ΔABC=

(14+x)(8)(6)x

So, 4(14+x)=

48x(14+x)

16(14+x)

2

=48x(14+x)

14+x=3x

2x=14⇒x=7

So, AB=6+x=6+7=13cm

AC=8+x=8+7=15cm

Sum = 13+15=28cm