AP EAMCET · Maths · Properties of Triangles
If \(I\) is the incentre of \(\triangle A B C\) and \(P_1, P_2, P_3\) are respectively the radii of the circumcircles of the \(\triangle I B C, \triangle I C A\) and \(\triangle I A B\), then \(P_1 P_2 P_3=\)
- A \(2 R r\)
- B \(2 R r^2\)
- C \(2 R^2 r\)
- D \(\frac{4 R}{r}\)
Answer & Solution
Correct Answer
(C) \(2 R^2 r\)
Step-by-step Solution
Detailed explanation
In \(\triangle I B C, \angle B I C=\frac{\pi}{2}-\frac{A}{2}\), let circumcentre of \(\triangle I B C\) is \(C_1\), then \(\angle B C_1 C=\frac{\pi}{2}+\frac{A}{2}\) So, \(\quad \frac{a / 2}{P_1}=\sin \left(\frac{\pi}{2}+\frac{A}{2}\right)=\cos \frac{A}{2}\)…
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