Question

ABC is a right-angled triangle right angled at A. A circle is inscribed in it the lengths of the two sides containing the right angle are 6 cm and 8 cm. Find the radius of the circle. [4 MARKS]

Answer 1

Concept: 1 Mark
Application: 1 Mark
Calculation : 2 Marks

Using Pythagoras theorem for $\Delta BAC$, we have

${BC}^2={AB}^2+{AC}^2$

$\Rightarrow {BC}^2=6^2+8^2=100\Rightarrow BC=10cm$

Now, Area of $\Delta ABC=Areaof\Delta OAB+Areaof\Delta OBC+Areaof\Delta OCA$

$\frac{1}{2}AB\times AC=\frac{1}{2}AB\times r+\frac{1}{2}BC\times r+\frac{1}{2}CA\times r$

$\frac{1}{2}\times 6\times 8=\frac{1}{2}(6\times r)+\frac{1}{2}(10\times r)+\frac{1}{2}(8\times r)$

$\Rightarrow 24=3r+5r+4r$

$\Rightarrow 24=12r$

$\Rightarrow r=2cm$