Difference between revisions of "Power of a point theorem"

(Case 1 (Inside the Circle):)
(Statement:)
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==Statement:==
 
==Statement:==
  
There are three unique cases for this theorem.
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There are three unique cases for this theorem. Each case expresses the relationship between the length of line segments that pass through a common point and touch a circle in at least one point.
  
  

Revision as of 13:21, 23 April 2024

Statement:

There are three unique cases for this theorem. Each case expresses the relationship between the length of line segments that pass through a common point and touch a circle in at least one point.


Case 1 (Inside the Circle):

If two chords $AB$ and $CD$ intersect at a point $P$ within a circle, then $AP\cdot BP=CP\cdot DP$

Case 2 (Outside the Circle):

Case 3 (On the Border/Useless Case):

    • Still working