Question

If in ∆ABC, the line joining the circum-centre and the in-

centre is parallel to BC, then-

• A. r = R sin A
• B. R = r sin A
• C. r = R cos A
• D. R = r cos A

Answer 1

Answer: (C)

r = R cos A

Answer 2

Let S be the circum-centre and I, the in-centre of ∆ABC. Since SI || BC, IN = SM ⇒ SM = r,

Also SB = R and BSM = A!

∴ from ∆SBM, cos A = $\frac{SM}{SB}$= $\frac{r}{R}$

⇒ r = R cos A