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Triangle ABC is equilateral with side length 1.  Let P be a point on the incircle of triangle ABC.  Compute PA^2 + PB^2 + PC^2.

 Jan 24, 2021
 #1
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Triangle ABC is equilateral with side length 1.  Let P be a point on the incircle of triangle ABC.  Compute PA^2 + PB^2 + PC^2.

 

PA2 + PB2 + PC2 = 1.25

 Jan 24, 2021
 #2
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I have assumed that the answer will be the same where ever P is put.   (P is on the incircle of course)

 

The easiest place to put P is on the midpoint of one of the sides.

 

Now all the distances are really easy to find.  

I will leave that to you though. 

 

 Jan 27, 2021

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