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Sir pls solve the following.
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Asked by rsudipto | 05 Jan, 2019, 09:20: AM
answered-by-expert Expert Answer
begin mathsize 18px style straight r subscript 1 comma straight r subscript 2 comma straight r subscript 3...... exradii comma straight a comma straight b comma straight c space sides space of space increment straight s equals semiperimeter straight r equals fraction numerator area increment over denominator straight s end fraction straight r subscript 1 equals fraction numerator area increment over denominator straight s minus straight a end fraction straight r subscript 2 equals fraction numerator area increment over denominator straight s minus straight b end fraction straight r subscript 3 equals fraction numerator area increment over denominator straight s minus straight c end fraction straight r plus straight r subscript 1 equals straight r subscript 2 plus straight r subscript 3.......... given fraction numerator area increment over denominator straight s end fraction plus fraction numerator area increment over denominator straight s minus straight a end fraction equals fraction numerator area increment over denominator straight s minus straight b end fraction plus fraction numerator area increment over denominator straight s minus straight c end fraction 1 over straight s plus fraction numerator 1 over denominator straight s minus straight a end fraction equals fraction numerator 1 over denominator straight s minus straight b end fraction plus fraction numerator 1 over denominator straight s minus straight c end fraction fraction numerator 2 straight s minus straight a over denominator straight s open parentheses straight s minus straight a close parentheses end fraction equals fraction numerator 2 straight s minus straight b minus straight c over denominator open parentheses straight s minus straight b close parentheses open parentheses straight s minus straight c close parentheses end fraction sub space straight s equals fraction numerator straight a plus straight b plus straight c over denominator 2 end fraction fraction numerator straight b plus straight c over denominator straight a end fraction equals fraction numerator straight b squared plus straight c squared minus straight a plus 2 bc over denominator negative straight b squared minus straight c squared plus straight a plus 2 bc end fraction fraction numerator straight b plus straight c over denominator straight a end fraction equals fraction numerator begin display style fraction numerator straight b squared plus straight c squared minus straight a over denominator 2 bc end fraction end style plus 1 over denominator negative open parentheses fraction numerator straight b squared plus straight c squared minus straight a over denominator 2 bc end fraction close parentheses plus 1 end fraction fraction numerator straight b squared plus straight c squared minus straight a over denominator 2 bc end fraction equals cosA fraction numerator straight b plus straight c over denominator straight a end fraction equals fraction numerator begin display style 1 plus cosA end style over denominator 1 minus cosA end fraction componendo fraction numerator straight a plus straight b plus straight c over denominator straight a end fraction equals fraction numerator begin display style 2 end style over denominator 1 minus cosA end fraction straight s over straight a equals fraction numerator begin display style 1 end style over denominator 1 minus cosA end fraction now straight A greater than straight pi over 3 also space straight A less than straight pi....... straight A thin space is space vertex space of space triangle so straight pi over 3 less than straight A less than straight pi 1 half less than cos space straight A less than 0 max space value space of space cos space straight A space equals space 1 half min space value space of space cos space straight A space equals space minus 1 so space max space value space of space straight s over straight a space equals space fraction numerator begin display style 1 end style over denominator 1 minus begin display style 1 half end style end fraction equals 2 min space value space of space straight s over straight a space equals space fraction numerator begin display style 1 end style over denominator 1 minus open parentheses negative 1 close parentheses end fraction equals 1 half end style
Answered by Arun | 18 Jan, 2019, 10:24: AM

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