InterviewSolution
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InterviewSolution
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In ` A B C`, the coordinates of the vertex `A`are `(4,-1)`, and lines `x-y-1=0`and `2x-y=3`are the internal bisectors of angles `Ba n dC`. Then, the radius of the encircle of triangle `A B C`is`4/(sqrt(5))`(b) `3/(sqrt(5))`(c) `6/(sqrt(5))`(d) `7/(sqrt(5))`A. `4//sqrt(5)`B. `3//sqrt(5)`C. `6//sqrt(5)`D. `7//sqrt(5)` |
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Answer» Correct Answer - C Incentre I is point of intersection of two angle bisectors which is (2,1). `IA = sqrt(2^(2) + 2^(2)) = 2 sqrt(2)` `"Also, AI" = r " cosec" (A)/(2)` `angleBIC = (pi)/(2) + (A)/(2)` `"or tan"((pi)/(2)+(A)/(2)) = |(1-2)/(1+2)|` `"or tan "(A)/(2) = 3` `"So, r" = (AI)/("cosec"(A)/(2)) = (2sqrt(2))/(sqrt(1+(1)/(9))) (2sqrt(2) xx 3)/(sqrt(10)) = (6)/(sqrt(5))` |
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