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Kasturi Abhishek Murthy
Asked: 2022-11-07T22:53:00+05:30 In:

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

A circle of radius 4 cm is inscribed in `DeltaABC`, which touches side BC at D. If BD = 6 cm, DC = 8 cm then
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)`
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  1. 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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