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July 21st, 2009, 08:30 PM  #1 
Newbie Joined: Jul 2008 From: Barnaul, Russia Posts: 18 Thanks: 0  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) =? I do not need an answer as much as i need the way of solving it. Please help out. 
July 22nd, 2009, 02:03 AM  #2 
Global Moderator Joined: Dec 2006 Posts: 20,931 Thanks: 2207 
By first finding the midpoints 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 midpoint of AC in this case. 
July 22nd, 2009, 04:54 AM  #3 
Newbie Joined: Jul 2008 From: Barnaul, Russia Posts: 18 Thanks: 0  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.. how do i find those with such info. Please help out. 
July 22nd, 2009, 05:08 AM  #4 
Newbie Joined: Jul 2008 From: Barnaul, Russia Posts: 18 Thanks: 0  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! 
July 22nd, 2009, 02:03 PM  #5 
Global Moderator Joined: Dec 2006 Posts: 20,931 Thanks: 2207 
You made a slip when calculating the slope of BC.

July 24th, 2009, 06:03 PM  #6 
Member Joined: May 2009 Posts: 37 Thanks: 0  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?

July 25th, 2009, 03:16 AM  #7 
Global Moderator Joined: Dec 2006 Posts: 20,931 Thanks: 2207 
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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circl, circle, find, inscribed, origin, triangle 
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