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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 ______.
Options
`1/sqrt(A)`
`2/sqrt(A)`
`3/sqrt(A)`
`sqrt(A)/2`
MCQ
Fill in the Blanks
Solution
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)`
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Properties of Triangle
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