Question

Find the radius of the circle inscribed in a rhombus with diagonals of length 12 and 16 ?

• A. 5.2
• B. 10
• C. 4.8
• D. None of these

Answer 1

Answer: (C)

Let $d_1=12$ and $d_2=16$ be the length of diagonals and ' $a$ ' be the side of Rhombus and $r=$ radius of inscribed circle.
Using Pythagoras theorem

$a=\sqrt{(\frac{d_1}{2}{)}^2+(\frac{d_2}{2}{)}^2}$
$\Rightarrow a=\sqrt{(\frac{12}{2}{)}^2+(\frac{16}{<}br/>2{)}^2}=\sqrt{6^2+8^2}=\sqrt{100}$
$\Rightarrow a=10$
$\text{ Area of Rhombus }=\frac{d_1{d}_2}{2}\text{ and }2ar$

$\text{ ia }$
$2ar\text{ is derived using }=\text{ area of rhombus }=$
$4\times \text{ area of triangle }$
$\text{ Area of Rhombus }=4\times \frac{1}{2}\times a\times r=2ar$
$\text{ Using (i), we get }$
$\frac{d_1{d}_2}{2}=2ar$
$\frac{12\times 16}{2}=2\times 10\times r$
$r=\frac{16\times 6}{2\times 10}\Rightarrow r=4.8$