In the given figure, `ABC` is a right-angled triangle with `AB=6cm` and `AC=8cm`. A circle with centre `O` has been inscribed inside the triangle. Calculate the value of `r`, the radius of the inscribed circle.

Explanation

Join `OA` , `OB` and `OC`
Draw `OD bot AB`, `OE bot BC` and `OF bot CA`.
Then, `OD=OE=OF=rcm`.
`:.ar(DeltaABC)=(1)/(2)xxABxxAC=((1)/(2)xx6xx8)cm^(2)=24cm^(2)`
Now, `ar(DeltaABC)=(1)/(2)xx("perimeter of" DeltaABC)xxr`
`implies24=(1)/(2)xx(AB+BC+CA)xxr`
`implies24=(1)/(2)xx(6+10+8)xxrimpliesr=2` [`:. BC^(2)=AB^(2)+AC^(2)impliesBC=sqrt(6^(2)+8^(2))=10`]
Hence, the radius of the inscribed circle is `2cm`.