In an equilateral triangle ABC- the ratio of 3Rr isHere- R and r are the radii of circumcircle and incircle respectively-

We know that in an nbsp;equilateral triangle ABC, a=b=c Now, nbsp;3Rr=3×abc4ΔΔs ⇒3Rr=3a^3s4Δ^2 ⇒3Rr=3a^3×3a24Δ^2 ⇒3Rr=9a^48×316× a^4 ∴3Rr=6 ...

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Standard XII

Mathematics

Factorization Method Form to Remove Indeterminate Form

In an equilat...

Question

In an equilateral triangle $A B C,$ the ratio of $\frac{3 R}{r}$ is
(Here, $R$ and $r$ are the radii of circumcircle and incircle respectively.)

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Solution

We know that in an equilateral triangle $A B C,$ $a = b = c$
Now, $\frac{3 R}{r} = \frac{3 \times \frac{a b c}{4 Δ}}{\frac{Δ}{s}}$
$\Rightarrow \frac{3 R}{r} = \frac{3 a^{3} s}{4 Δ^{2}}$
$\Rightarrow \frac{3 R}{r} = \frac{3 a^{3} \times \frac{3 a}{2}}{4 Δ^{2}}$
$\Rightarrow \frac{3 R}{r} = \frac{9 a^{4}}{8 \times \frac{3}{16} \times a^{4}}$
$∴ \frac{3 R}{r} = 6$

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In an equilateral triangle ABC, the ratio of 3Rr is (Here, R and r are the radii of circumcircle and incircle respectively.)

We know that in an equilateral triangle ABC, a=b=c Now, 3Rr=3×abc4ΔΔs ⇒3Rr=3a3s4Δ2 ⇒3Rr=3a3×3a24Δ2 ⇒3Rr=9a48×316×a4 ∴3Rr=6

In an equilateral triangle $A B C,$ the ratio of $\frac{3 R}{r}$ is
(Here, $R$ and $r$ are the radii of circumcircle and incircle respectively.)