# Center of Triangel - Incentre Proof?

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Hi there, I was just wondering how to obtain the solution for the center point of a triangle. I can work out the radius for the incenter triangle and I've got one or two books with the solution in, but am having problems working it out step by step. This is the example I'm using: http://www.terra.es/personal/rgonzal1/incentre.htm If you look at that example, I'm okay upto where it gets: ku - mv = Q - P = PQ. But then how he gets the coefficient value of k! If someone could just expand on this it would be great :) Thanks, Ben

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Why do you wanna do that?

Simple center of triangle:

c = (p0 + p1 + p2) / 3

where 'c' is center and 'p0', 'p1', 'p2' are triangle vertices

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If you do:

c = (p0 + p1 + p2) / 3

This is called the cetner of gravity of the triangle, not the incenter.

There are different methods for triangle centers:
Incenter,
Circumcenter,
Centrolid, etc

Wanted to know the proof of the equation for the incenter equation. Which is:

C = |p2-p3|p1 + |p3-p1|p2 + |p1-p2|p3 / Perimeter{p1p2p3}

Thanks,

Ben

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It looks like he is leaving steps out. He is showing steps for the vertex P up to that point. If you do similar steps for the other two vertices you will have three equations, and three unknowns. You should then be able to solve for any/all of the constants.

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Ben,

Your problem appears to be academic in nature, rather than purely related to game development. Note that this is primarily a game development forum, rather than a general-purpose math forum. It is possible that I've misinterpreted your post, but you haven't given enough information for me to judge otherwise.

Since you've just registered yesterday, please take a look at the Forum FAQ for this forum, which explains the forum policy on academic (schoolwork/homework/etc.) type topics.

Since it looks like you're asking for a proof, but haven't really made any comment as to how this is an on-topic (game development) post, and haven't shown us your own personal progress in detail, I'm going to close the thread.

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