Find the circumcircle radius $ R $ of a hexagon if incircle radius $r = 18$.
Answer
$R = 12 \sqrt{ 3 }$
Explanation
STEP 1: find side $ a $
To find side $ a $ use formula:
$$ r = \dfrac{ \sqrt{ 3 } \cdot a }{ 2 } $$After substituting $ r = 18 $ we have:
$$ 18 = \dfrac{ \sqrt{ 3 } \cdot a }{ 2 } $$ $$ \sqrt{ 3 } \cdot a = 18 \cdot 2 $$ $$ \sqrt{ 3 } \cdot a = 36 $$ $$ a = \dfrac{ 36 }{ \sqrt{ 3 } } $$ $$ a = 12 \sqrt{ 3 } $$STEP 2:
The radius of the circumcircle is equal the side of the hexagon. $$ R = 12 \sqrt{ 3 } $$
This page was created using
Hexagon Calculator