In-an-equilateral-triangle-with-usual-notations-the-value-of-27r-2-R-r-1-r-2-r-3-is-equal-to-

Question Number 18847 by Tinkutara last updated on 30/Jul/17

In an equilateral triangle with usual

notations the value of \frac{27 r^{2} R}{r_{1} r_{2} r_{3}} is equal to

Answered by behi.8.3.4.1.7@gmail.com last updated on 31/Jul/17

i n e q u i l a t e r a l t r i a n g l e :

1) R = 2 r = \frac{a}{2 s i n A} = \frac{a}{2 \times \frac{\sqrt{3}}{2}} = a . \frac{\sqrt{3}}{3}

2) r_{1} = r_{2} = r_{3} = p . t g \frac{A}{2} = \frac{3 a}{2} . \frac{\sqrt{3}}{3} = a \frac{\sqrt{3}}{2}

\Rightarrow \frac{27 r^{2} R}{Π r_{1}} = \frac{27 \times \frac{a^{2}}{12} \times a \frac{\sqrt{3}}{3}}{a^{3} \times \frac{3 \sqrt{3}}{8}} = 2 .

Commented by Tinkutara last updated on 31/Jul/17

Thank you very much behi Sir!