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10 grade maths> circle with centre A and radius 3,circle ...

question mark

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

Matt Farrel , 10 Years ago

Grade 10

1 Answers

Jitender Singh

Last Activity: 10 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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