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Intermediate

Triangular billiards

A ball track starts halfway the left side of an equilateral triangular billiard table having side length 2. After two bounces it arrives in the top corner. What’s the total track length?

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Solution

The total track length is √13.

Like in The corner pocket, the key in this solution is the mirror trick. In this case the length of the line segment EF can be found using the cosine rule in triangle AEF: |EF|2=1+16-2*4*cos(60°)=13.

Poem

A triangular billiard table
Is just for gamer who are able
To play the game together
Every day better and better
Putting the billiard ball
With the cue stick hit them all.
Billiard is quite like life
The game does not last
It passes fast
One breathe
One second

Bella

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