Question

In usual notation a ΔABC, if A, A₁, A₂, A₃ be the area of the in-circle and ex-circles, then `1/sqrt(A_1) + 1/sqrt(A_2) + 1/sqrt(A_3)` is equal to ______.

पर्याय

• `1/sqrt(A)`

• `2/sqrt(A)`

• `3/sqrt(A)`

• `sqrt(A)/2`

Answer 1

In usual notation a ΔABC, if A, A₁, A₂, A₃ be the area of the in-circle and ex-circles, then `1/sqrt(A_1) + 1/sqrt(A_2) + 1/sqrt(A_3)` is equal to `underlinebb(1/sqrt(A))`.

Explanation:

`1/sqrt(A_1) + 1/sqrt(A_2) + 1/sqrt(A_3)`

= `1/sqrt(πr_1^2) + 1/sqrt(πr_2^2) + 1/sqrt(πr_3^2)`

= `1/sqrt(π)(1/r_1 + 1/r_2 + 1/r_3)`

= `1/sqrt(π)(s - a + s - b + s - c)/Δ`

= `1/sqrt(π).s/Δ`

= `1/sqrt(π). 1/r`

= `1/sqrt(πr^2)`

= `1/sqrt(A)`