Question
Find the incircle radius $ r $ of a hexagon if circumcircle radius $R = 14\, \text{cm}$.
Answer
$7 \sqrt{ 3 }\, \text{cm}$
Explanation
STEP 1:
The side of the hexagon is equal the radius of the circumcircle. $$ a = 14 $$
STEP 2: find incircle radius $ r $
To find incircle radius $ r $ use formula:
$$ r = \dfrac{ \sqrt{ 3 } \cdot a }{ 2 } $$After substituting $a = 14\, \text{cm}$ we have:
$$ r = \dfrac{ \sqrt{ 3 } \cdot 14\, \text{cm} }{ 2 } $$$$ r = \dfrac{ 14 \sqrt{ 3 }\, \text{cm} }{ 2 } $$ $$ r = 7 \sqrt{ 3 }\, \text{cm} $$This page was created using
Hexagon Calculator