InterviewSolution
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InterviewSolution
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In `Delta ABC`, if a = 10 and `b cot B + c cot C = 2(r + R)` then the maximum area of `DeltaABC` will beA. 50B. `sqrt50`C. 25D. 5 |
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Answer» Correct Answer - C `b cot B + c cot C = 2 (r + R)` `rARr 2R sin B .(cosB)/(sinB) + 2R sin C.(cos C)/(sinC) = 2(r + R)` `rArr cos B + cos C = 1 + (r)/(R)` `rArr cos B + cos C = 1 + 4 sin.(A)/(2) sin.(B)/(2) sin.(C)/(2)` `rArr cos B + cos C = cos A + cos B + cos C` `:. cos A = 0` `rArr A = (pi)/(2)` `rArr a^(2) = b^(2) + c^(2)` `rArr b^(2) + c^(2) = 100` Using A.M. `ge` G.M. we get `(b^(2) + c^(2))/(2) ge sqrt(b^(2) c^(2))` `rArr bc le 50` Hence, area of `Delta ABC = (1)/(2) bc le 25` |
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