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The ex – radii r 1 , r 2 , r 3 of ∆ ABC are in H. P. Show that its sides a, b, c are in A. P.

The ex – radii r1, r2, r3 of ∆ ABC are in H. P. Show that its sides a, b, c are in A. P.

Grade:11

1 Answers

Aditi Chauhan
askIITians Faculty 396 Points
6 years ago
Hello Student,
Please find the answer to your question
KEY CONCEPT:
Ex – radii of a ∆ABC are r1­ = ∆/s – a, r2 = ∆/s – b
r3 = ∆/s – c As r1, r2, r3 are in H. P. ∴ 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 A. P.

Thanks
Aditi Chauhan
askIITians Faculty

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