# Thread: regular hexagon

1. ## regular hexagon

three of the six vertices of regular hexagon are chosen at random.the possibility that the triangle with three vertices is equilateral equals

three vertices can be chosen as 6C3 after that what to do

2. i think we can take central angle of regular hexagon and by angle in a segment=half central angle we can judge whether the triangle is equilateral or not

3. Hello, prasum!

I don't suppose you made a sketch . . .

Three of the six vertices of regular hexagon are chosen at random.
Find the probability that the three vertices form an equilateral triangle.

Three vertices can be chosen as 6C3. . Right!
After that, what to do?

. . $\begin{array}{ccccc}
&& A \\
F &&&& B \\ && * \\
E &&&& C \\
&& D \end{array}$

There are only two equilateral triangles: . $ACE$ and $BDF.$

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# Three of six vertices of a regular hexagon are choosen at random. Find the probability that the triangle with three vertices is equilateral?

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