Question

In triangle ABC, I is the incentre of the triangle. If ‘R’ and ‘r’ be the circumradius and inradius, then (AI) (BI) (CI) is equal to –

• A. 4r² R
• B. 4R² r
• C. r² R
• D. R² r

Answer 1

Answer: (A)

4r² R

Answer 2

AI = r cosec A/2, BI = r cosec B/2

CI = r cosec C/2

Ž AI . BI . CI =

= = 4R r²

[Q r = 4R sin A/2 sin B/2 sin C/2].