Question

In a DABC, let ĐC = $\frac { \pi } { 2 }$ . If r is the inradius and R is the circumradius of the triangle, then 2(r + R) is equal to –

• A. a + b
• B. b + c
• C. c + a
• D. a + b + c

Answer 1

Answer: (A)

a + b

Answer 2

Let C be origin, M

R² = MC² = $\frac { 1 } { 4 }$ (a² + b²) = $\frac { 1 } { 4 }$ c²

̃ R = c/2

r = (s – c) tan C/2 = (s – c) tan p/4 = s – c

̃ 2(r + R) = 2r + 2R = 2s – 2c + c

= a + b + c – 2c + c

= a + b.