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.

nathanl6656 Sep 20, 2024

#1**+1 **

We can essentially complete this problem with a nice and simply graph.

Here, I borrowed Melody's.

In the yellow area, it is where the point would satisfy the conditions given in the problem.

As shown, we have split the graph into triangles.

There are 18 congruent triangles here, with 12 of them are in the yellow zone.

Thus, we have a \( 12/18 = 2/3\) chance.

Thanks! :)

NotThatSmart Sep 21, 2024