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Let ABC be an equilateral triangle.  A point P is chosen at random inside triangle ABC.  Find the probability that P is closer to vertex A than to vertex B.

 Jul 25, 2022
 #1
avatar+2321 
+1

Let the side of the triangle be \(2s\)

 

The area of "success" is a \(60 ^ \circ\) sector of a circle centered at Point A, and the radius is half the side length of the triangle. 

 

The total area is the area of an equilateral triangle. 

 

Can you take it from here?

 Jul 26, 2022
 #2
avatar+117766 
+2

Thanks Builderboi.

 

Here is another way of looking at it.

 

Since it is a equilateral triangle, the point is just as likely to be closer to A as it is to be closer to B

 

what does that tell you. 

 Jul 27, 2022

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