Finding the Incenter of a TriangleDate: 10/08/2006 at 17:58:54 From: Eli Subject: Finding the Incenter of a Triangle Hi, I am wondering what is the equation to find the incenter of a triangle? I do not understand the Cartesian Coordinates of the incenter. Date: 10/08/2006 at 18:52:15 From: Doctor Philip Subject: Re: Finding the Incenter of a Triangle Hi Eli, One way to find the incenter of a triangle in the Cartesian plane is to use the fact that it is equidistant from all three sides. If you find the equations of all three sides of the triangle, and put them into standard form, you can then use the formula for the distance between a point and a line to find the incenter. For example, if two of the sides are a1(x) + b1(y) = c1 a2(x) + b2(y) = c2 Note: the numbers are subscripts then a point is on the bisector of the angle formed by these two lines is |a1(x) + b1(y) - c1| |a2(x) + b2(y) - c2| -------------------- = -------------------- sqrt((a1)^2+(b1)^2) sqrt((a2)^2+(b2)^2) You can write a similar equation using two other sides of the triangle. Finding the intersection between the two bisectors yields the incenter. Please write back if you have any more questions on this topic. - Doctor Philip, The Math Forum http://mathforum.org/dr.math/ Date: 10/09/2006 at 11:23:26 From: Eli Subject: Thank you (Finding the Incenter of a Triangle) Thanks for your help. It helped me understand incenters in a very easy way. |
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