My Math Forum Need assistance with solving a triangle

 Algebra Pre-Algebra and Basic Algebra Math Forum

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]circle-solve-01a.png[/attachmentmil1qpd]

Any ideas on how to solve this?
Thanks!

-Kim
Attached Images
 circle-solve-02.png (68.3 KB, 106 views) circle-solve-01a.png (7.2 KB, 106 views)

 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. $(rA+rC)^2=(rA+rB)^2+(rB+rC)^2-2*(rA+rB)*(rB+rC)*\cos {\gamma}$ 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 "short-cuts": 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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