If the perimeter of the triangle formed by feet of altitudes of the triangle ABC is equal to four times the circumradius of `Delta ABC`, then identify the type of `Delta ABC`

Answer

Triangle is not possible

Explanation

AD, BE and CF are altitudes.

`DE = c cos C, EF = a cos A, FD = b cos B`
Given that `4R = a cos A + b cos B + c cos C`
`rArr 4R = R (sin 2A + sin 2B + sin 2C)`
`rArr sin A sin B sin C =1`
This is possible only when `angle A = angle B = angle C = pi//2`
So, triangle is not possible