A circle of radius 4 cm is inscribed in `DeltaABC`, which touches side BC at D. If BD = 6 cm, DC = 8 cm thenA. the triangle is necessarily acute angledB. `tan.(A)/(2) = (4)/(7)`C. perimeter of the triangle ABC is 42 cmD. area of `DeltaABC " is " 84 cm^(2)`

A circle of radius 4 cm is inscribed in `DeltaABC`, which touches side

1.	A circle of radius 4 cm is inscribed in `DeltaABC`, which touches side BC at D. If BD = 6 cm, DC = 8 cm thenA. the triangle is necessarily acute angledB. `tan.(A)/(2) = (4)/(7)`C. perimeter of the triangle ABC is 42 cmD. area of `DeltaABC " is " 84 cm^(2)`
Answer» Correct Answer - A::B::C::D `"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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A circle of radius 4 cm is inscribed in `DeltaABC`, which touches side BC at D. If BD = 6 cm, DC = 8 cm thenA. the triangle is necessarily acute angledB. `tan.(A)/(2) = (4)/(7)`C. perimeter of the triangle ABC is 42 cmD. area of `DeltaABC " is " 84 cm^(2)`

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