In ∆ABC, If r1=8, r2=12, r3=24,Show that a=12,b=16,c=20. (From 

Asked by Soma | 4th Mar, 2019, 11:18: PM

Expert Answer:

In ΔABC, r1 = 8, r2 = 12, r3 = 24
begin mathsize 16px style 1 over straight r equals 1 over straight r subscript 1 plus fraction numerator begin display style 1 end style over denominator begin display style straight r subscript 2 end style end fraction plus fraction numerator begin display style 1 end style over denominator begin display style straight r subscript 3 end style end fraction
fraction numerator begin display style 1 end style over denominator begin display style straight r end style end fraction equals fraction numerator begin display style 1 end style over denominator begin display style 8 end style end fraction plus fraction numerator begin display style 1 end style over denominator begin display style 12 end style end fraction plus fraction numerator begin display style 1 end style over denominator begin display style 24 end style end fraction
fraction numerator begin display style 1 end style over denominator begin display style straight r end style end fraction equals fraction numerator 3 plus 2 plus 1 over denominator 24 end fraction
fraction numerator begin display style 1 end style over denominator begin display style straight r end style end fraction equals 1 fourth
straight r equals 4
increment equals square root of rr subscript 1 straight r subscript 2 straight r subscript 3 end root equals square root of 4 cross times 8 cross times 12 cross times 24 end root equals 96
straight r equals increment over straight s equals 96 over straight s
fraction numerator begin display style 96 end style over denominator begin display style straight s end style end fraction equals 4
straight s equals 24
straight r subscript 1 equals fraction numerator increment over denominator straight s minus straight a end fraction equals fraction numerator 96 over denominator 24 minus straight a end fraction equals 8
fraction numerator begin display style 96 end style over denominator begin display style 24 minus straight a end style end fraction equals 8
12 equals 24 minus straight a
straight a equals 12
Similarly comma space using space straight r subscript 2 equals fraction numerator 96 over denominator 24 minus straight b end fraction equals 12 space and space straight r subscript 3 equals fraction numerator begin display style 96 end style over denominator begin display style 24 minus straight c end style end fraction equals 24 space we space get space straight b equals 16 space and space straight c equals 20

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Answered by Sneha shidid | 5th Mar, 2019, 09:30: AM