Q47. The radius of the inner circle of a triangle
is 4 cm and the segments into which one side is
divided by the point of contact are 6 cm and
cm, Then other two sides of the triangle are.
Answers
Answer:
ANSWER
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
=21×4(6+x)+21×4(14)+21×4(8+x)
=21×4(28+2x)
=4(14+x)
Also, area of ΔABC by Heron's formula
S=214+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+
Step-by-step explanation:
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Answer:
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
Step-by-step explanation:
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