Find the probability that the point P is closer to the centroid than the sides.

Asked Jun 30 '20 at 06:30

Active Jul 01 '20 at 18:46

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A point 'P' is picked uniformly at random inside a regular hexagon. Find the probability that the point P is closer to the centroid than the sides.

I came to know from this site that if that's a equilateral triangle, the formula is =3^(-1)–3^(-2)–3^(-3) But how can I use this formula when the figure is regular hexagon ?

edited Jul 01 '20 at 18:46

asked Jun 30 '20 at 06:30

Mathematician

A circle doesn't sound right. You'll probably need some parabolas. Definitely draw a diagram and test a few points to get a feel for it! – Chris Culter Jun 30 '20 at 06:38
1

In fact this is the $n=6$ case of https://math.stackexchange.com/a/1706984 – Chris Culter Jun 30 '20 at 06:43

Find the probability that the point P is closer to the centroid than the sides.

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