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August 18th, 2013, 08:17 AM  #1 
Newbie Joined: Aug 2013 Posts: 8 Thanks: 0  Need assistance with solving a triangle
Hey guys, Here's a drawing to help illustrate what I'm trying to accomplish: [attachment=0mil1qpd]circlesolve01a.png[/attachmentmil1qpd] Any ideas on how to solve this? Thanks! Kim 
August 18th, 2013, 08:40 AM  #2 
Senior Member Joined: Mar 2012 From: Belgium Posts: 654 Thanks: 11  Re: Need assistance with solving a triangle
Using the cosine rule you get this. Do you see how I got to this ? Can you solve this equation for rC now ? 
August 18th, 2013, 09:10 AM  #3 
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 14,141 Thanks: 1003  Re: Need assistance with solving a triangle
You can reduce "the work" quite a bit with following "shortcuts": Let the radii = a and b and c . Since a and b plus angle y are GIVENS, then let u = a+b and v = COS(y) Then (as shown by my gf Jelly!): (a + c)^2 = u^2 + (b + c)^2  2uv(b + c) a^2 + 2ac + c^2 = u^2 + b^2 + 2bc + c^2  2uvb  2 uvc Notice the c^2 on both sides will cancel out: sooooo take over 
August 22nd, 2013, 09:02 AM  #4 
Newbie Joined: Aug 2013 Posts: 8 Thanks: 0  Re: Need assistance with solving a triangle
Thanks guys. Somehow I had forgotten all about solving polynomials ^^


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