Question
Find the circumcircle radius $ R $ of a hexagon if short diagonal $s = \frac{ 7 }{ 16 }\, \text{cm}$.
Answer
$\dfrac{ 7 \sqrt{ 3}}{ 48 }\, \text{cm}$
Explanation
STEP 1: find side $ a $
To find side $ a $ use formula:
$$ s = \sqrt{ 3 } \cdot a $$After substituting $s = \dfrac{ 7 }{ 16 }\, \text{cm}$ we have:
$$ \frac{ 7 }{ 16 }\, \text{cm} = \sqrt{ 3 } \cdot a $$ $$ a = \dfrac{ \frac{ 7 }{ 16 }\, \text{cm} }{ \sqrt{ 3 } } $$ $$ a = \frac{ 7 \sqrt{ 3}}{ 48 }\, \text{cm} $$STEP 2:
The radius of the circumcircle is equal the side of the hexagon. $$ R = \frac{ 7 \sqrt{ 3}}{ 48 } $$
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