Thank you Sr! :)
I love geometry. I made pen-and-paper game based on geometry, would share it with you if you are interested.

We have a winner!

Oh yes, those square holes. I had seen a little sketch of that thing, never saw it in action. Cool!

south_korea_ln

I love the Reuleaux triangle so much. It's used in industry to 

 of the ABC inscribed triangle is 6cm because of how the Reuleaux triangle is composed. That allows us to get the center position 

 from any vertex, for it's equal to 2/3 of the triangle's height 

science

[Daily puzzle] Reuleaux triangle

I love the Reuleaux triangle so much. It's used in industry to [drill squared holes](https://www.youtube.com/watch?app=desktop&v=Hf2T0AFSaqE)! How crazy is that!!

**Solution**:

So, each segment $$ s $$ of the ABC inscribed triangle is 6cm because of how the Reuleaux triangle is composed. That allows us to get the center position $$ p $$ from any vertex, for it's equal to 2/3 of the triangle's height $$ h $$, thus:

$$ s = 6 cm $$

$$ h = sen(60°) \cdot s = { \sqrt{3} \over 2 } \cdot s $$

$$ p = { 2 \over 3 } h = { \sqrt{3} \over 3 } \cdot s $$

So, the radius $$ r $$ of the inscribed circle is:

$$ r = s - p = s - { \sqrt{3} \over 3 } \cdot s = s \cdot \left( 1 - { \sqrt{3} \over 3 } \right) $$

So in numbers:

$$ r = 2 \cdot \left( 3 - { \sqrt{3}  } \right) cm = 2.536 cm$$