
Algebra PreAlgebra and Basic Algebra Math Forum 
 LinkBack  Thread Tools  Display Modes 
August 9th, 2010, 02:12 PM  #1 
Newbie Joined: Aug 2010 Posts: 1 Thanks: 0  Angular Circle Intersection
I am looking for a method to solve the problem in the below image, generally. Ideally I would like to find a formula for both the start and extent angles of the arc. The following formulas produce the xy coordinates of the intersection points: x = ([x1x2][r12r22x12+x22]+[x1+x2][y1y2]2+[y1y2]sqrt[Delta])/(2[x1x2]2+2[y1y2]2), y = ([y1y2][r12r22y12+y22]+[y1+y2][x1x2]2[x1x2]sqrt[Delta])/(2[x1x2]2+2[y1y2]2), and x = ([x1x2][r12r22x12+x22]+[x1+x2][y1y2]2[y1y2]sqrt[Delta])/(2[x1x2]2+2[y1y2]2), y = ([y1y2][r12r22y12+y22]+[y1+y2][x1x2]2+[x1x2]sqrt[Delta])/(2[x1x2]2+2[y1y2]2), where Delta = ([x1x2]2+[y1y2]2[r1r2]2)([x1x2]2+[y1y2]2[r1+r2]2). I used the law of cosines to find the angular starting point of the arc, but the rounding was unacceptable for acute angles. While the solution currently eludes me, I feel there must be a fundamental relationship here that is easily computed by formula to find the angular circle intersection of the arc. 
August 15th, 2010, 03:08 AM  #2 
Member Joined: Aug 2010 From: Osijek Posts: 33 Thanks: 0  Re: Angular Circle Intersection
I found this problem interesting, so I worked on it for a while. And this is what I concluded: Now, I forgot that you need a starting point too, so I'll try and find an optimal solution soon. Oh and sorry for posting this in .jpg images, I failed to see the "latex" button on forum. 

Tags 
angular, circle, intersection 
Search tags for this page 
Click on a term to search for related topics.

Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
union of intersection, intersection of unions  annakar  Applied Math  1  January 7th, 2013 03:16 PM 
Ellipse inside a circle  intersection  Andromedus  Algebra  18  February 3rd, 2012 12:03 PM 
Test the intersection of a rectangle and a circle  andirrashi  Algebra  3  October 24th, 2011 07:38 AM 
Find intersection of a Circle with Yaxis...  horees  Algebra  2  December 18th, 2009 12:51 PM 
Points of intersection of a circle.  Oxymoron  Algebra  4  July 23rd, 2008 04:11 PM 