Question

The legs of a right angled triangle are 8 cm and 15 cm. The radius of the circle inscribed in the triangle (in cm), is _________.

• A. 1
• B. 2
• C. 3
• D. 4

Answer 1

The correct option is C 3

Area of $△ABC=\frac{1}{2}\times 15\times 8=60{cm}^2$

Now, $r$ is the radius of the incircle of the circle.

Now consider,

(Area of $△AIB$+Area of $△BIC$+Area of $△CIA$)$=\frac{1}{2}\times 15\times 8=60$

$=>\frac{1}{2}\times AB\times r+\frac{1}{2}\times BC\times r+\frac{1}{2}\times AC\times r=60=>\frac{1}{2}\times r\times {(AB+BC+AC)}^2=60=>\frac{1}{2}\times r\times 20=60=>r=3cm$