
Algebra PreAlgebra and Basic Algebra Math Forum 
 LinkBack  Thread Tools  Display Modes 
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: 20,379 Thanks: 2011 
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: 20,379 Thanks: 2011 
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: 20,379 Thanks: 2011 
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.


Tags 
circl, circle, find, inscribed, origin, triangle 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Largest possible inscribed triangle in a circle  Daltohn  Calculus  11  October 27th, 2013 08:19 AM 
find radius if a circle is inscribed in quadrilateral  amitdixit  Algebra  1  August 25th, 2012 08:49 PM 
Irregular polygon inscribed in a circle, find radius  Zappo  Algebra  4  May 11th, 2012 12:37 AM 
Find origin of this circle?  colinbeaton1  Algebra  2  January 16th, 2011 12:56 PM 
Largest possible inscribed triangle in a circle  Daltohn  Algebra  0  December 31st, 1969 04:00 PM 