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# Probability

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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.

Jun 1, 2024

#1
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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

Jun 1, 2024
edited by NotThatSmart  Jun 1, 2024

#1
+806
+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
edited by NotThatSmart  Jun 1, 2024
#2
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Very nice......this one always stumped me  !!!!

CPhill  Jun 1, 2024
#3
+806
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I mean, it is credits to Melody. Her answer helped me understand it!

NotThatSmart  Jun 1, 2024