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If-in-ABC-m-B-3m-C-then-a-b-c-b-c-1-b-gt-a-c-2-R-c-3-3c-b-




Question Number 175081 by Shrinava last updated on 18/Aug/22
If in △ABC , m(∢B)=3m(∢C) then:  a = (b − c) (√((b/c) + 1))  ,  b > a + (c/2)  R = (√(c^3 /(3c − b)))
$$\mathrm{If}\:\mathrm{in}\:\bigtriangleup\mathrm{ABC}\:,\:\mathrm{m}\left(\sphericalangle\mathrm{B}\right)=\mathrm{3m}\left(\sphericalangle\mathrm{C}\right)\:\mathrm{then}: \\ $$$$\mathrm{a}\:=\:\left(\mathrm{b}\:−\:\mathrm{c}\right)\:\sqrt{\frac{\mathrm{b}}{\mathrm{c}}\:+\:\mathrm{1}}\:\:,\:\:\mathrm{b}\:>\:\mathrm{a}\:+\:\frac{\mathrm{c}}{\mathrm{2}} \\ $$$$\mathrm{R}\:=\:\sqrt{\frac{\mathrm{c}^{\mathrm{3}} }{\mathrm{3c}\:−\:\mathrm{b}}} \\ $$

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