Posted by **kelly** on Monday, April 20, 2009 at 9:04pm.

with only have the points on a triangle how would you determine the radius and center of the incircle of that triangle?

- math -
**Reiny**, Monday, April 20, 2009 at 9:41pm
There are 4 centres of a triangle,

the centroid, the orthocentre, the circumcentre and the incentre.

of those four you asked for the hardest one to find, lol

By definition, the incentre is the point in a triangle which is equidistant from each of the three sides

Are you familiar with the formula for finding the distance from a given point to a given line?

The distance from (p,q) to the line Ax + By + C = 0

= |Ap +Bq + C|/√(A^2+B^2)

so find the equation of each of the 3 sides of the triangle and write them in the general form

Ax+By+C=0

then using your given point, find 3 different expressions for the distance.

They must all be equal.

form 2 equations by setting any two of the expressions equal to each other.

That will give you 2 equations containing p and q.

solve.

Good luck, this is usually a very messy problem unless it was carefully planned.

(If somebody has a better way to do this, I would appreciate letting me know)

- math -
**kelly**, Tuesday, April 21, 2009 at 12:07am
The general form of the equations are (4/3)x+y=(1688/3)

(-9/40)x+y=(19577/40)

(5/12)x+y=(-3929/12)

but then when I use the incenter(p,q)and express it for distance and set the equations equal to each other i get different things when I set the first 2 equations together than I do the second 2 and the first and last. Can you tell me what I am doing wrong?

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