Question

The radius of the circle passing through the centre of the in-circle of DABC and through the end points of BC is given by-

• A. $\frac{a}{2}$cosA
• B. $\frac{a}{2}$sec $\frac{A}{2}$
• C. $\frac{a}{2}$sin A
• D. a sec $\frac{A}{2}$

Answer 1

Answer: (B)

$\frac{a}{2}$sec $\frac{A}{2}$

Answer 2

Đ BOC = 2p – (p + A)

$\left[ \because \angle \mathrm { BIC } = \pi - \frac { \mathrm { B } + \mathrm { C } } { 2 } = \frac { \pi } { 2 } + \frac { \mathrm { A } } { 2 } \right]$

= p – A

Q a² = R² + R² – 2R² cos (p – A)

\ a² = 2R²(1+ cos A)

R = = $\frac { \mathrm { a } } { 2 }$ sec $\frac { \mathrm { A } } { 2 }$