Circumradius of `DeltaABC` is 3 cm and its area is `6 cm^(2)`. If DEF is the triangle formed by feet of the perpendicular drawn from A,B and C on the sides BC, CA and AB, respectively, then the perimeter of `DeltaDEF` (in cm) is _____

Answer

4

Explanation

Perimeter of `DeltaDEF = a cos A + b cos B + c cos C`
`= R [sin 2A + sin 2B + sin 2C]`
`= R [4 sin A sin B sin C]`
`= 4R (abc)/(8R^(3)) = (abc)/(2R^(2)) = (2 Delta)/(R) = 4 cm`