InterviewSolution
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InterviewSolution
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In an acute angled triangle ABC, `r + r_(1) = r_(2) + r_(3) and angleB gt (pi)/(3)`, thenA. `b + 2c lt 2a lt 2b + 2c`B. `b + 4cc lt 4a lt 2b + 4c`C. `b + 4c lt 4a lt 4b + 4c`D. `b + 3c lt 3a lt 3b + 3c` |
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Answer» Correct Answer - D `r - r_(2) = r_(3) -r_(1)` `rArr (Delta)/(s) - (Delta)/(s-b) = (Delta)/(s-c) -(Delta)/(s-a)` or `(-b)/(s(-b)) = (c-a)/((s-a) (s-c))` or `((s-a) (s-c))/(s(s-b)) = (a-c)/(b)` `rArr tan^(2).(B)/(2) = (a-c)/(b)` But `(B)/(2) in ((pi)/(6), (pi)/(4))`. Therefore, `tan^(2).(B)/(2) in ((1)/(3),1)` `rArr (1)/(3) lt (a-c)/(b) lt 1` or `b lt 3a -3c lt 3b` or `b + 3c lt 3a lt 3b + 3c` |
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