1.

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

Answer»

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

Solution :`"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


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