Question

In-circle of radius 4 cm of a triangle ABC touches the side BC at D. If BD = 6cm., DC = 8 cm, then the area of the

triangle ABC is-

• A. 42 cm²
• B. 84 cm²
• C. $\frac { 84 } { 3 }$ cm²
• D. None of these

Answer 1

Answer: (B)

84 cm²

Answer 2

We have ∠ IBD = , ∠ ICD =

BD = 6 cm, CD = 8 cm ⇒ BC = a = 14 cm. Also, ID = r = 4 cm

Now, tan= $\frac { 4 } { 6 }$ = $\frac { 2 } { 3 }$ and tan= $\frac { 4 } { 8 }$= $\frac { 1 } { 2 }$

tan tan = $\sqrt { \frac { ( s - a ) ( s - c ) } { s ( s - b ) } }$ × =

∴ $\frac { 2 } { 3 }$ × $\frac { 1 } { 2 }$ = ⇒ s = 21 cm

∴ Area, ∆ = rs = 4 × 21 = 84 cm²