If in a `!ABC` ,b = 12 units , c = 5 units and `!`= 30 sq. units , then the distance between vertex A and incentre of the triangle is equal to

Options

A. 2 units
B. `2sqrt2` units
C. `sqrt2` units
D. none of these

Explanation

We know that the distance of the vertex A from the incentre I is given by
`IA=r/(sinA/2)`
We have,
`Delta=30 ` sq. units
`rArr=1/2bcsinA=30rArr12xx5sinA=60rArra=pi/2`
`thereforea^(2)=b^(2)+c^(2)rArra^(2)=12^(2)+5^(2)=169rArra=13`
Now,
`IA=r/(sinA/2)`
`rArrIA=(Delta)/scosecpi/4rArrIA=30/((13+12+5)/2))xxsqrt2=2sqrt2` units