Triangle Incentre rectangular co-ordinates.

[onta...@hotmail.com]

Find the incentre of the triangle formed by the lines whose equations are
3x-4y = 0
4x+3y-8 = 0
24x-7y-12 = 0

[shy author]

GP-Pari finds the vertices to be located at

? P1 = [32/25, 24/25]
? P2 = [16/25, 12/25]
? P3 = [23/25, 36/25]

and corresponding opposite side lengths are

a1 = 1
a2 = 3/5
a3 = 1

and using the formula posted at http://en.wikipedia.org/wiki/Incircle for
the coordinates of the incentre, we find

incentre = [ 323/325, 336/325 ]

If the formula is correct then the incentre has been given.

[onta...@hotmail.com]

No, but fairly close.

[shy author]

> On Fri, 04 Jul 2008 13:49:56 +0000, onta...@hotmail.com wrote:
>
>> Find the incentre of the triangle formed by the lines whose equations
>> are 3x-4y = 0
>> 4x+3y-8 = 0
>> 24x-7y-12 = 0
>
> GP-Pari finds the vertices to be located at
>
> ? P1 = [32/25, 24/25]
> ? P2 = [16/25, 12/25]
> ? P3 = [23/25, 36/25]
>
> and corresponding opposite side lengths are
>
> a1 = 1
> a2 = 3/5
> a3 = 1

whoops. Due to a transcription error, the length of a3 is not 1, it is
4/5

After using the correct value for a3, the incentre is at [1,1] if I have
not made another mistake

[onta...@hotmail.com]

That is correct.