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circle with centre A and radius 3,circle with centre B and radius 24,circle with centre C and radius 27 touch each other externally i.e every circle touches the remaining two circles.Find the inradius of triangle ABC

circle with centre A and radius 3,circle with centre B and radius 24,circle with centre C and radius 27 touch each other externally i.e every circle touches the remaining two circles.Find the inradius of triangle ABC

Grade:10

1 Answers

Jitender Singh IIT Delhi
askIITians Faculty 158 Points
9 years ago
Ans:
Hello Student,
Please find answer to your question below

You have the sides of triangle ABC ehich is the sum of radius.
a = 24 + 27 = 51
b = 3 + 27 = 30
c = 3 + 24 = 27

Inradius r
r = \frac{1}{2}\sqrt{\frac{(a+b-c)(b+c-a)(c+a-b)}{a+b+c}}
r = \frac{1}{2}\sqrt{\frac{(51+30-27)(30+27-51)(27+51-30)}{51+30+27}}
r = \frac{1}{2}\sqrt{\frac{54.6.48}{108}}
r = \frac{1}{2}\sqrt{\frac{6.6.4}{1}}
r = \frac{1}{2}.6.2 = 6

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