1.

Right triangle ABC with right angle A has an area equal to its perimeter. If the incentre of the triangle ABC is I and IB is of length sqrt(13), find its area (in sq. units).

Answer»

Solution :`rcosec(B)/(2)=sqrt(13)`
ALSO, `Delta=rs`
but `Delta=2s("given")`
`:.r=2`
Hence `"sin"(B)/(2)=(2)/(sqrt(13))`
`:.cosB=1-2"sin"^(2)(B)/(2)=1-(8)/(13)=(5)/(13)`

now using
`2s=Delta`
`30K=(5K.12K)/(2)`
`:.""k=1`
hence area of `Delta=30` SQ. units.


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