Question

Find the radius of the incircle of $△ABC\text{if}BC\perp AQ$

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

Answer 1

The correct option is B

2 cm

Triangle ABC is a right angled triangle ...( Given)
$A{B}^2=B{C}^2+A{c}^2=6^2+8^2$
...( Pythagoras Theorem )
AB = 10 ~ cm ...( Pythagoras triplet 6 - 8 - 10 )

Semi-perimeter $△ABC$,
$s=\frac{a+b+c}{2}=\frac{6+8+10}{2}=12cm$

Area of $△ABC,A=\frac{1}{2}\times 6\times 8=24c{m}^2$

Radius of the Incircle,
$r=\frac{A}{s}=\frac{24}{12}=2cm.$