In an equilateral , form (where symbols have usual meanings) leckgq f=Hkqt ,

JEE MainMathematicsEasyProperties of triangle

In an equilateral $\Delta ABC,r,R,r_{1}$ , form (where symbols
have usual meanings)
leckgq f=Hkqt $\Delta ABC,$ $r,R,r_{1}$ ,

Show answer and solution

a = b = c \Rightarrow s = \frac{3a}{2}

r = (s - a)tan\frac{A}{2} = \frac{a}{2\sqrt{3}}

R = \frac{abc}{4\Delta} = \frac{a^{3}}{\sqrt{3}a^{2}} = \frac{a}{\sqrt{3}} = \frac{2a}{2\sqrt{3}}

r_{1} = Stan\frac{A}{2} = \frac{3a}{2\sqrt{3}}

\therefore r,R,r_{1},\ form\ an\ AP

Source: Grass-G / M-26 Mathematics Paper 1 15 Jan.docx

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