If `I_(1), I_(2), I_(3)` are the centers of escribed circles of `Delta ABC`, show that the area of `Delta I_(1) I_(2) I_(3)` is (abc)/(2r)`

Explanation

Area `= (I_(1) I_(2) xx I_(3)I_(2) xx I_(1) I_(3))/(4R')`
where R' = Circumradius of `Delta I_(1) I_(2) I_(3)`
`= ((4R cos.(A)/(2)) (4R cos.(B)/(2))(4R cos.(C)/(2)))/(8R)` (`:' Delta ABC` is pedal triangle for `Delta I_(1), I_(2), I_(3)`)
`=8R^(2) cos.(A)/(2) cos.(B)/(2) cos.(C)/(2)`
`= (R^(2) sin A sin B sin C)/(sin.(A)/(2) sin.(B)/(2) sin.(C)/(2))`
`= (R^(2) abc)/(8R^(3) sin.(A)/(2) sin.(B)/(2) sin.(C)/(2))`
`= (abc)/(2(4R sin.(A)/(2) sin.(B)/(2) sin.(C)/(2)))`
`= (abc)/(2r)`