A circle of radius 4 cm is inscribed in `DeltaABC`, which touches side BC at D. If BD = 6 cm, DC = 8 cm then

Options

A. the triangle is necessarily acute angled
B. `tan.(A)/(2) = (4)/(7)`
C. perimeter of the triangle ABC is 42 cm
D. area of `DeltaABC " is " 84 cm^(2)`

Answer

A, B, C, D

Explanation

`"tan"(B)/(2) = (2)/(3), "tan"(C)/(2) = (1)/(2) rArr tan.(A)/(2) = (4)/(7)`,
`rArr "tan"(B)/(2) "tan"(C)/(2) = (s-a)/(s) = (1)/(3)`
`rArr 2s = 3a = 42`
`:. Delta = rs = 84 cm^^(2)`
Thus, `"tan"(A)/(2), "tan"(B)/(2), "tan"(C)/(2)` all are less than 1
Hence, all angles of the triangle are acute