My Math Forum Triangle inscribed in a circle. Find the origin of the circl

 Algebra Pre-Algebra and Basic Algebra Math Forum

 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 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.
 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.

 Tags circl, circle, find, inscribed, origin, triangle

 Thread Tools Display Modes Linear Mode

 Similar Threads Thread Thread Starter Forum Replies Last Post Daltohn Calculus 11 October 27th, 2013 08:19 AM amitdixit Algebra 1 August 25th, 2012 08:49 PM Zappo Algebra 4 May 11th, 2012 12:37 AM colinbeaton1 Algebra 2 January 16th, 2011 12:56 PM Daltohn Algebra 0 December 31st, 1969 04:00 PM

 Contact - Home - Forums - Cryptocurrency Forum - Top