In an equilateral triangle the in-radius...

In an equilateral triangle the in-radius and the circum-radius are connected by

A

r=4R

B

`r=R/2`

C

`r=R/3`

D

none of these

Text Solution

AI Generated Solution

To find the relationship between the in-radius (r) and the circum-radius (R) of an equilateral triangle, we can follow these steps: ### Step-by-Step Solution 1. **Understanding the Triangle**: Let the side length of the equilateral triangle be \( a \). In an equilateral triangle, all sides are equal. 2. **Calculating the Area (Δ)**: ...

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In an equilateral triangle the inradius and the circum-radius is connected by (1)r=4R(2)r=(R)/(2)(3)r=(R)/(3)(4)r=(r)/(sqrt(3))

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Knowledge Check

In an equilateral triangle of sides 2sqrt3 cm the circum-radius is

A

`1 cm`

B

`sqrt3 cm`

C

`2 cm`

D

`2sqrt3 cm`

In an equilaterial triangle of side 2sqrt3 cms, the circum-radius ,is

A

1cm

B

`sqrt3` cm

C

2cm

D

`2sqrt3` cm

For an equilateral triangle, the ratio of the in-radius and the ex radius is

A

`1 : 2`

B

`1:sqrt(2)`

C

`1:3`

D

`1 : sqrt(3)`

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