Triangle XYZ is equilateral, with O as its center. A point P is chosen at random. Find the probability that P is closer to point O than to any of the side lengths.

Stanry Aug 9, 2024

#1**+1 **

Ok! This one is pretty easy!

To make this problem way easier, we have a graph!

Anyways, we have triangles in this graph!

First off, let's note that the yellow part is the part that would satisfy the statements made in the problem.

Now, we can note we have a lot of triangles. There are a few ays we could fo this, but I like to note that we have multiple 30-60-90 triangles. Each unshaded region is made up of 2, for more a more specific answer.

Now, we can easily tell that there are 18 30-60-90 triangles in this graph. (I counted them all)

If we count the triangles only in the shaded region, we can count 12 of them!

Meaning, we just have

Thanks! :) :) :)

NotThatSmart Aug 9, 2024