question on incircle

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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.

Guest Jan 24, 2021

Guest · Answer 1 · 2021-01-24T04:47:57

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

Melody · Answer 2 · 2021-01-27T07:09:57

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.