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.

magenta Jun 1, 2024

#1**+1 **

Let's draw a diagram.

The Green part is where the points would satisfy the conditions.

There are 18 triangles congruent to each other in this graph. If we count, 12 of them are in the green area.

Thus, we have \(\frac{12}{18} = \frac{2}{3}\)

Thanks! :)

~Oh, and thank you Melody for the graph

NotThatSmart Jun 1, 2024

#1**+1 **

Best Answer

Let's draw a diagram.

The Green part is where the points would satisfy the conditions.

There are 18 triangles congruent to each other in this graph. If we count, 12 of them are in the green area.

Thus, we have \(\frac{12}{18} = \frac{2}{3}\)

Thanks! :)

~Oh, and thank you Melody for the graph

NotThatSmart Jun 1, 2024