Concurrencies of a triangle

Gavin "shels"

In the middle of doing my maths homework, and just can't seem to get my head around "Concurrencies of a triangle". Can anyone example to me how to do them, for people who are in 5th there on Page.61 on Concise Maths 4.

Please help,
Gavin

PurpleFistMixer

What exactly is the question you're having difficulty with?

Gavin "shels"

Find the coordinates of the circumcentre of each of the triangles, whose vertices are: (-2,2) (-4,-2) (5,-5).



Find the coordinates of the orthocentre of each of the triangles, whose vertices are: (2,2) (4,1) (1,5).

PurpleFistMixer

Hmm. I don't recall ever doing something like that in coordinate geometry of the line, if that's what you're doing.

The first one could be solved if you've done geometry of the circle, use the formula x^2 + y^2 + 2gx + 2fy + c = 0 where the centre is (-g, -f) and substitute in with your three vertices to find the three variables.

Second one.. I can't think offhand of a simple way to do that, sorry I cannae help any more!

Nanaki

I think the circumcentre is the point through which the perpendicular bisector of each vertice and/or angle meet, not fully sure.

ZorbaTehZ

Cicumcentre is the intersection of the perpendicular bisectors of the lines.
Orthocentre is the intersection of lines from a vertex perpendicular to the opposite side.

Are you using Texts & Tests? 'Tis well described in that.

Gavin "shels"

ZorbaTehZ wrote: »

Cicumcentre is the intersection of the perpendicular bisectors of the lines.
Orthocentre is the intersection of lines from a vertex perpendicular to the opposite side.

Are you using Texts & Tests? 'Tis well described in that.

Spot on.

No I'm using Concise Maths, might buy that book aswell.

kulva

yes its done very well in texts and tests. good maths book all round really.