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 Š IBD = $\frac { B } { 2 }$ , Š ICD =

BD = 6 cm, CD = 8 cm Ž BC = a = 14 cm.

Also, ID = r = 4 cm

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

tan $\frac { B } { 2 }$ tan = $\sqrt { \frac { ( s - a ) ( s - c ) } { s ( s - b ) } }$ × =

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

\ Area, D = rs = 4 × 21 = 84 cm²