• Status: Solved
• Priority: Medium
• Security: Public
• Views: 345

finding triangle circumcentre with equations for the triangle sides

Hi

I'm trying to find the triangle circumcentre from the equations for the triangle sides. I don't think I'm doing it right as I can't see how to finish the question off.

To get the circumcentre I need the point of intersection of 2 perpendicular bisectors. Given the equation of the side, the gradient of the bisector is -1/m but i don;t know how to get a point on this line to then work out the equation for the line using y - y1 = m(x - x1). I could say that the midpoint of the side is ((x1 + x2)/2, (y1 + y2)/2) and this point is on the perpendicular bisector but i don't know how to put this knowledge into y - y1 = m(x - x1). There's too many different x and y variables.

Once i have got the equation for one bisector i can get the others and then solve these equations simulataneously to get the midpoint.

The equations of the triangle are
y = 3x
y + 3x = 0
3y -x +12 = 0

Many thanks
0
andieje
• 4
• 4
• 2
• +2
1 Solution

Author Commented:
perhaps i need the coordinates of the corners first?
0

Author Commented:
I can't get anything right today.

Are the corners A (0,0), B = (1.5, 4.5), C= (-1.2,3.6)
and midpoints AB = (0.75, 2.25), AC (-0.6, 1.8), BC(0.15, 4.05)

thanks
0

Commented:
Something is wrong here
y = 3x
y + 3x = 0
3y -x +12 = 0
The first two lines are parallel to each other, hence the third cannot make a triangle.
0

Author Commented:
no they aren't!
0

Commented:
y = 3x
y = -3x
you are right
0

Commented:
Note that the perpendicular bisector of line 2 is parallel to line 3
0

Commented:
Solve systems of all equations pairwise and you will get corners coordinates. For example, 1st and 2nd give (0,0).
0

Commented:
and perp bi of line 3 is parallel to line 2
0

Author Commented:
Hi, that's what I did. Got the corners and then the bisectors. Thanks
0

Commented:
I answered this one for someone earlier, but the question was slightly different.  I think the solution is the same.

Use this after figuring out your corners.

http://www.experts-exchange.com/Other/Math_Science/Q_25045192.html?cid=1131#a26286230
0

Commented:
Are you sure you accepted the correct answer? It was just a hint. Have you find the circumcentre?
0

Commented:
andieje,

here's a no-point site of interest - has all sorts of visual aids:
http://www.mathopenref.com/trianglecircumcenter.html
http://www.mathopenref.com/constcircumcircle.html

0

Featured Post

• 4
• 4
• 2
• +2
Tackle projects and never again get stuck behind a technical roadblock.