Find the incircle radius $r$ of an equilateral triangle if circumcircle radius $R = 2.12 cm$ .

Answer

$1.06 cm$

Explanation

STEP 1: find side $a$

To find side $a$ use formula:

R = \frac{3 \cdot a}{3}

After substituting $R = 2.12 cm$ we have:

2.12 cm = \frac{3 \cdot a}{3}

3 \cdot a = 2.12 cm \cdot 3

3 \cdot a = 6.36 cm

a = \frac{6.36 cm}{3}

a \approx 3.6719 cm

STEP 2: find incircle radius $r$

To find incircle radius $r$ use formula:

r = \frac{3 \cdot a}{6}

After substituting $a = 3.6719 cm$ we have:

r = \frac{3 \cdot 3.6719 cm}{6}

r = \frac{6.36 cm}{6}

r = 1.06 cm

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Find the incircle radius r of an equilateral triangle if circumcircle radius R=2.12cm.

1.06cm

Find the incircle radius $r$ of an equilateral triangle if circumcircle radius $R = 2.12 cm$ .

$1.06 cm$