Question

The ex-radii  r₁, r₂, r₃ of ∆ABC are in HP, show that its sides a,b,c are in AP.

Answer 1

Since, r₁, r₂, r₃ are ex-radii of ∆ ABC are in HP

∴ 1/r₁, 1/r₂, 1/r₃ are in AP

⇒ (s - a)/∆, (s - b)/∆,(s - c)/∆ are in AP

⇒ s – a, s – b, s – c are in AP

⇒ – a, – b, – c are in AP

⇒ a, b, c are in AP