Question

In ΔABC, right angled at B, BC = 15 cm and AB = 8 cm. A circle is inscribed in ΔABC. The radius of the circle is:

• A. 2 cm
• B. 4 cm
• C. 1 cm
• D. 3 cm

Answer 1

Answer:

D. 3 cm

In ΔABC, ∠B = 90°

⇒ AC² = AB² + BC²

⇒ AC = √(64 + 225) = √289= 17 cm

Now area of ΔABC = $\frac{1}{2}\times{AB}\times{BC}$

$=\frac{1}{2}\times{8}\times{15}$ = 60 cm²

Let the radius of circle is r and centre is I.

Then area of (ΔAIB + ΔAIC + ΔBIC) = 60

⇒ [$\frac{1}{2}\times{AB}\times{r}+\frac{1}{2}\times{r}\times{AC}+\frac{1}{2}\times{r}\times{BC}$] = 60

⇒ $\frac{1}{2}(8\times{r}+17\times{r}+15\times{r})$ = 60

⇒ 40r = 120

∴ r = 3 cm