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 graviton120 July 21st, 2009 08:30 PM

Triangle inscribed in a circle. Find the origin of the circl

Hey guys,
I have a problem:
If the center of the circle which is circumscribed around the triangle is M(x,y) and the vertices of the inscribed triangle are: A(-1,-3) B(1,1) and C(9,-3) then the coordiantes of the M(x,y) =?

 skipjack July 22nd, 2009 02:03 AM

By first finding the mid-points and the slopes of two sides of the triangle, find the equations of the perpendicular bisectors of those sides, then solve those equations to find M(x, y).

Is that sufficient help?

Shortcut solution: if you plot the given points on a graph, you can see that M happens to be the mid-point of AC in this case.

 graviton120 July 22nd, 2009 04:54 AM

Re: Triangle inscribed in a circle. Find the origin of the circl

ok so i found mids for
AB = (0,-1)
BC = (5,-1)
slopes for AB = 2
BC = -2/5
I am stuck with perpendicular bisectors..

 graviton120 July 22nd, 2009 05:08 AM

Re: Triangle inscribed in a circle. Find the origin of the circl

oh i think i got it, perpendiculars are -(inverse)
so slope AB (perp) =-1/2
BC (perp) = 5/2
Thanks!

 skipjack July 22nd, 2009 02:03 PM

You made a slip when calculating the slope of BC.

 SteveThePirate July 24th, 2009 06:03 PM

Re: Triangle inscribed in a circle. Find the origin of the circl

I am actually kind of interested in knowing the last step, i could do all of the other things, how does knowing the perpendicular bisector help you find the center?

 skipjack July 25th, 2009 03:16 AM

That's where the perpendicular bisectors intersect, since any point on the perpendicular bisector of a line is equidistant from the endpoints of the line.

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