Question
Find the circumcircle radius $ R $ of a hexagon if incircle radius $r = 18\, \text{cm}$.
Answer
$12 \sqrt{ 3 }\, \text{cm}$
Explanation
STEP 1: find side $ a $
To find side $ a $ use formula:
$$ r = \dfrac{ \sqrt{ 3 } \cdot a }{ 2 } $$After substituting $r = 18\, \text{cm}$ we have:
$$ 18\, \text{cm} = \dfrac{ \sqrt{ 3 } \cdot a }{ 2 } $$ $$ \sqrt{ 3 } \cdot a = 18\, \text{cm} \cdot 2 $$ $$ \sqrt{ 3 } \cdot a = 36\, \text{cm} $$ $$ a = \dfrac{ 36\, \text{cm} }{ \sqrt{ 3 } } $$ $$ a = 12 \sqrt{ 3 }\, \text{cm} $$STEP 2:
The radius of the circumcircle is equal the side of the hexagon. $$ R = 12 \sqrt{ 3 } $$
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