AP EAMCET · Maths · Properties of Triangles
In a \(\triangle A B C\), let \(\angle C=\frac{\pi}{2}\). If \(r\) and \(R\) are respectively inradius and circumradius of \(A B C\), then \(R+r=\)
- A \(\frac{a-b}{2}\)
- B \(\frac{a+b}{2}\)
- C \(a+b\)
- D \(a-b\)
Answer & Solution
Correct Answer
(B) \(\frac{a+b}{2}\)
Step-by-step Solution
Detailed explanation
\[ x+y=2 R \] Now, \[ \begin{array}{ll} & a+b=x+r+y+r=2 R+2 r \\ \therefore & R+r=\frac{a+b}{2} \end{array} \]
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