Question

If the area of triangle DABC is a² – (b – c)² then its circum radius R =

• A. a/16 cosec² (A/2)
• B. (C/16) sin² (C/2)
• C. a/6 sin² (A/2)
• D. b/16 sin² (B/2)

Answer 1

Answer: (A)

a/16 cosec² (A/2)

Answer 2

D = a² – (b – c)² = a² – b² – c² + 2bc

cos A = $\frac { \mathrm { b } ^ { 2 } + \mathrm { c } ^ { 2 } - \mathrm { a } ^ { 2 } } { 2 \mathrm { bc } }$ = = $1 - \frac { \Delta } { 2 b c }$

= $1 - \frac { a b c } { 4 R \times 2 b c }$ = 1 –

̃ 8R = $\frac { a } { 1 - \cos A }$ =

̃ R = cosec² .