Find the circumcircle radius $ R $ of a hexagon if incircle radius $r = \frac{ 16 }{ 125 }$.
Answer
$R = \frac{ 32 \sqrt{ 3}}{ 375 }$
Explanation
STEP 1: find side $ a $
To find side $ a $ use formula:
$$ r = \dfrac{ \sqrt{ 3 } \cdot a }{ 2 } $$After substituting $ r = \frac{ 16 }{ 125 } $ we have:
$$ \frac{ 16 }{ 125 } = \dfrac{ \sqrt{ 3 } \cdot a }{ 2 } $$ $$ \sqrt{ 3 } \cdot a = \frac{ 16 }{ 125 } \cdot 2 $$ $$ \sqrt{ 3 } \cdot a = \frac{ 32 }{ 125 } $$ $$ a = \dfrac{ \frac{ 32 }{ 125 } }{ \sqrt{ 3 } } $$ $$ a = \frac{ 32 \sqrt{ 3}}{ 375 } $$STEP 2:
The radius of the circumcircle is equal the side of the hexagon. $$ R = \frac{ 32 \sqrt{ 3}}{ 375 } $$
This page was created using
Hexagon Calculator