
Geometry Geometry Math Forum 
 LinkBack  Thread Tools  Display Modes 
February 15th, 2010, 02:33 PM  #1 
Newbie Joined: Feb 2010 Posts: 1 Thanks: 0  Geometry: Circle Inversion and Power of P
Alright.. I'm going over circle inversion and power of P, for some reason something isn't clicking. The question is: (pretend the numerical values are the little sub values) Show that the product of PP1 and PP2 (or PQ1 and PQ2) can be expressed as PO^(2)  r^(2). Where P is the Power of P. I got the image off some website, so it's not the exact one that I have. Pretend that where O is, it's actually P.. and pretend that there is a point in the center of the circle called O. 
February 16th, 2010, 05:30 AM  #2 
Global Moderator Joined: Dec 2006 Posts: 20,370 Thanks: 2007 
I've seen that website; it does make sense, but perhaps the following will help. You acknowledge that PP1/PQ1 = PQ2/PP2, which is true since triangles PQ1P2 and PP1Q2 are similar. That still applies when Q1 and Q2 are the same point, Q, and so P1.P2 = PQ² = PO²  r² by Pythagoras, where r is the radius of the circle. 

Tags 
circle, geometry, inversion, power 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Matrix Inversion Problem (symbolic inversion)  ktalebian  Linear Algebra  2  September 2nd, 2013 09:27 AM 
Circle Geometry  AzraaBux  Geometry  1  May 30th, 2013 02:42 PM 
Discontinuity of a power serie on the circle of convergence  triple 0  Complex Analysis  4  April 6th, 2013 12:52 PM 
Power Series, Inversion  DonkeyKong  Complex Analysis  1  April 20th, 2012 04:04 PM 
Circle Geometry  BeckyRanRan  Geometry  5  October 30th, 2011 04:55 AM 