Sure thing. Feel free to share it here in ~science if that would make sense...

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

didiplaywell

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

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:

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