AP EAMCET · Maths · Properties of Triangles
If the reciprocals of the lengths of the sides of a \(\triangle A B C\) are in harmonic progression, then its ex-radii \(r_1, r_2, r_3\) are in
- A Arithmetic progression
- B Geometric progression
- C Harmonic progression
- D Arithmetico-geometric progression
Answer & Solution
Correct Answer
(C) Harmonic progression
Step-by-step Solution
Detailed explanation
Let the sides of a \(\triangle A B C\) are \(a, b\) and \(c\) \(\because \frac{1}{a}, \frac{1}{b}, \frac{1}{c}\) are in H.P. \(\Rightarrow a, b, c\) are in A.P. \(\Rightarrow s-a, s-b, s-c\) are in A.P. \(\Rightarrow \frac{s-a}{\Delta}, \frac{s-b}{\Delta}, \frac{s-c}{\Delta}\)…
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