AP EAMCET · Maths · Properties of Triangles
In \(\triangle A B C, \sqrt{\frac{r r_2}{r_3 r_1}}=\)
- A \(\left(r_3-r_2\right)\left(r_1-r_2\right)\)
- B \(r_3+r_1\)
- C \(\frac{b}{r_3-r_1}\)
- D \(\frac{b}{r_3+r_1}\)
Answer & Solution
Correct Answer
(D) \(\frac{b}{r_3+r_1}\)
Step-by-step Solution
Detailed explanation
\(\sqrt{\frac{r r_2}{r_3 r_1}} = \sqrt{\frac{(4R \sin(A/2) \sin(B/2) \sin(C/2))(4R \cos(A/2) \sin(B/2) \cos(C/2))}{(4R \cos(A/2) \cos(B/2) \sin(C/2))(4R \sin(A/2) \cos(B/2) \cos(C/2))}}\) \(= \sqrt{\frac{\sin^2(B/2)}{\cos^2(B/2)}} = \tan(B/2)\)…
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