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If \(r=\) in radius, \(\triangle=\) Area of \(\triangle A B C, s=\) semi-perimeter then which of the following is true?
Options:
Solution:
1874 Upvotes
Verified Answer
The correct answer is:
\(\Delta=r\) s
Let the length of sides are \(a, b\) and \(c\), so
\(s=\frac{a+b+c}{2}\)
Now, from the diagram area of triangle \(A B C\) is
\(\begin{aligned}
\Delta & =\Delta I B C+\Delta I C A+\Delta I A B \\
& =\frac{1}{2} a r+\frac{1}{2} b r+\frac{1}{2} c r \\
\Delta & =r\left(\frac{a+b+c}{2}\right)=r
\end{aligned}\)
Hence, option (d) is correct.
\(s=\frac{a+b+c}{2}\)
Now, from the diagram area of triangle \(A B C\) is
\(\begin{aligned}
\Delta & =\Delta I B C+\Delta I C A+\Delta I A B \\
& =\frac{1}{2} a r+\frac{1}{2} b r+\frac{1}{2} c r \\
\Delta & =r\left(\frac{a+b+c}{2}\right)=r
\end{aligned}\)
Hence, option (d) is correct.
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